Loan Analysis (Prosper Provided) by Andrew Teixeira

Load all relevant libraries

Establish working directory

#Establishing the working directory
getwd()
## [1] "/Users/andrewteixeira/Documents/DAND/Final_Project_EDA"

Load the data into the variable “loans”

Examining the column names of the dataset ‘loans’ to get a sense of what is within the dataset.

#Examing the column names of the dataset 'loans' to get a sense of what is within the dataset. 
names(loans)
##  [1] "ListingKey"                         
##  [2] "ListingNumber"                      
##  [3] "ListingCreationDate"                
##  [4] "CreditGrade"                        
##  [5] "Term"                               
##  [6] "LoanStatus"                         
##  [7] "ClosedDate"                         
##  [8] "BorrowerAPR"                        
##  [9] "BorrowerRate"                       
## [10] "LenderYield"                        
## [11] "EstimatedEffectiveYield"            
## [12] "EstimatedLoss"                      
## [13] "EstimatedReturn"                    
## [14] "ProsperRating..numeric."            
## [15] "ProsperRating..Alpha."              
## [16] "ProsperScore"                       
## [17] "ListingCategory..numeric."          
## [18] "BorrowerState"                      
## [19] "Occupation"                         
## [20] "EmploymentStatus"                   
## [21] "EmploymentStatusDuration"           
## [22] "IsBorrowerHomeowner"                
## [23] "CurrentlyInGroup"                   
## [24] "GroupKey"                           
## [25] "DateCreditPulled"                   
## [26] "CreditScoreRangeLower"              
## [27] "CreditScoreRangeUpper"              
## [28] "FirstRecordedCreditLine"            
## [29] "CurrentCreditLines"                 
## [30] "OpenCreditLines"                    
## [31] "TotalCreditLinespast7years"         
## [32] "OpenRevolvingAccounts"              
## [33] "OpenRevolvingMonthlyPayment"        
## [34] "InquiriesLast6Months"               
## [35] "TotalInquiries"                     
## [36] "CurrentDelinquencies"               
## [37] "AmountDelinquent"                   
## [38] "DelinquenciesLast7Years"            
## [39] "PublicRecordsLast10Years"           
## [40] "PublicRecordsLast12Months"          
## [41] "RevolvingCreditBalance"             
## [42] "BankcardUtilization"                
## [43] "AvailableBankcardCredit"            
## [44] "TotalTrades"                        
## [45] "TradesNeverDelinquent..percentage." 
## [46] "TradesOpenedLast6Months"            
## [47] "DebtToIncomeRatio"                  
## [48] "IncomeRange"                        
## [49] "IncomeVerifiable"                   
## [50] "StatedMonthlyIncome"                
## [51] "LoanKey"                            
## [52] "TotalProsperLoans"                  
## [53] "TotalProsperPaymentsBilled"         
## [54] "OnTimeProsperPayments"              
## [55] "ProsperPaymentsLessThanOneMonthLate"
## [56] "ProsperPaymentsOneMonthPlusLate"    
## [57] "ProsperPrincipalBorrowed"           
## [58] "ProsperPrincipalOutstanding"        
## [59] "ScorexChangeAtTimeOfListing"        
## [60] "LoanCurrentDaysDelinquent"          
## [61] "LoanFirstDefaultedCycleNumber"      
## [62] "LoanMonthsSinceOrigination"         
## [63] "LoanNumber"                         
## [64] "LoanOriginalAmount"                 
## [65] "LoanOriginationDate"                
## [66] "LoanOriginationQuarter"             
## [67] "MemberKey"                          
## [68] "MonthlyLoanPayment"                 
## [69] "LP_CustomerPayments"                
## [70] "LP_CustomerPrincipalPayments"       
## [71] "LP_InterestandFees"                 
## [72] "LP_ServiceFees"                     
## [73] "LP_CollectionFees"                  
## [74] "LP_GrossPrincipalLoss"              
## [75] "LP_NetPrincipalLoss"                
## [76] "LP_NonPrincipalRecoverypayments"    
## [77] "PercentFunded"                      
## [78] "Recommendations"                    
## [79] "InvestmentFromFriendsCount"         
## [80] "InvestmentFromFriendsAmount"        
## [81] "Investors"
head(loans)
##                ListingKey ListingNumber           ListingCreationDate
## 1 1021339766868145413AB3B        193129 2007-08-26 19:09:29.263000000
## 2 10273602499503308B223C1       1209647 2014-02-27 08:28:07.900000000
## 3 0EE9337825851032864889A         81716 2007-01-05 15:00:47.090000000
## 4 0EF5356002482715299901A        658116 2012-10-22 11:02:35.010000000
## 5 0F023589499656230C5E3E2        909464 2013-09-14 18:38:39.097000000
## 6 0F05359734824199381F61D       1074836 2013-12-14 08:26:37.093000000
##   CreditGrade Term LoanStatus          ClosedDate BorrowerAPR BorrowerRate
## 1           C   36  Completed 2009-08-14 00:00:00     0.16516       0.1580
## 2               36    Current                         0.12016       0.0920
## 3          HR   36  Completed 2009-12-17 00:00:00     0.28269       0.2750
## 4               36    Current                         0.12528       0.0974
## 5               36    Current                         0.24614       0.2085
## 6               60    Current                         0.15425       0.1314
##   LenderYield EstimatedEffectiveYield EstimatedLoss EstimatedReturn
## 1      0.1380                      NA            NA              NA
## 2      0.0820                 0.07960        0.0249         0.05470
## 3      0.2400                      NA            NA              NA
## 4      0.0874                 0.08490        0.0249         0.06000
## 5      0.1985                 0.18316        0.0925         0.09066
## 6      0.1214                 0.11567        0.0449         0.07077
##   ProsperRating..numeric. ProsperRating..Alpha. ProsperScore
## 1                      NA                                 NA
## 2                       6                     A            7
## 3                      NA                                 NA
## 4                       6                     A            9
## 5                       3                     D            4
## 6                       5                     B           10
##   ListingCategory..numeric. BorrowerState    Occupation EmploymentStatus
## 1                         0            CO         Other    Self-employed
## 2                         2            CO  Professional         Employed
## 3                         0            GA         Other    Not available
## 4                        16            GA Skilled Labor         Employed
## 5                         2            MN     Executive         Employed
## 6                         1            NM  Professional         Employed
##   EmploymentStatusDuration IsBorrowerHomeowner CurrentlyInGroup
## 1                        2                True             True
## 2                       44               False            False
## 3                       NA               False             True
## 4                      113                True            False
## 5                       44                True            False
## 6                       82                True            False
##                  GroupKey              DateCreditPulled
## 1                         2007-08-26 18:41:46.780000000
## 2                                   2014-02-27 08:28:14
## 3 783C3371218786870A73D20 2007-01-02 14:09:10.060000000
## 4                                   2012-10-22 11:02:32
## 5                                   2013-09-14 18:38:44
## 6                                   2013-12-14 08:26:40
##   CreditScoreRangeLower CreditScoreRangeUpper FirstRecordedCreditLine
## 1                   640                   659     2001-10-11 00:00:00
## 2                   680                   699     1996-03-18 00:00:00
## 3                   480                   499     2002-07-27 00:00:00
## 4                   800                   819     1983-02-28 00:00:00
## 5                   680                   699     2004-02-20 00:00:00
## 6                   740                   759     1973-03-01 00:00:00
##   CurrentCreditLines OpenCreditLines TotalCreditLinespast7years
## 1                  5               4                         12
## 2                 14              14                         29
## 3                 NA              NA                          3
## 4                  5               5                         29
## 5                 19              19                         49
## 6                 21              17                         49
##   OpenRevolvingAccounts OpenRevolvingMonthlyPayment InquiriesLast6Months
## 1                     1                          24                    3
## 2                    13                         389                    3
## 3                     0                           0                    0
## 4                     7                         115                    0
## 5                     6                         220                    1
## 6                    13                        1410                    0
##   TotalInquiries CurrentDelinquencies AmountDelinquent
## 1              3                    2              472
## 2              5                    0                0
## 3              1                    1               NA
## 4              1                    4            10056
## 5              9                    0                0
## 6              2                    0                0
##   DelinquenciesLast7Years PublicRecordsLast10Years
## 1                       4                        0
## 2                       0                        1
## 3                       0                        0
## 4                      14                        0
## 5                       0                        0
## 6                       0                        0
##   PublicRecordsLast12Months RevolvingCreditBalance BankcardUtilization
## 1                         0                      0                0.00
## 2                         0                   3989                0.21
## 3                        NA                     NA                  NA
## 4                         0                   1444                0.04
## 5                         0                   6193                0.81
## 6                         0                  62999                0.39
##   AvailableBankcardCredit TotalTrades TradesNeverDelinquent..percentage.
## 1                    1500          11                               0.81
## 2                   10266          29                               1.00
## 3                      NA          NA                                 NA
## 4                   30754          26                               0.76
## 5                     695          39                               0.95
## 6                   86509          47                               1.00
##   TradesOpenedLast6Months DebtToIncomeRatio    IncomeRange
## 1                       0              0.17 $25,000-49,999
## 2                       2              0.18 $50,000-74,999
## 3                      NA              0.06  Not displayed
## 4                       0              0.15 $25,000-49,999
## 5                       2              0.26      $100,000+
## 6                       0              0.36      $100,000+
##   IncomeVerifiable StatedMonthlyIncome                 LoanKey
## 1             True            3083.333 E33A3400205839220442E84
## 2             True            6125.000 9E3B37071505919926B1D82
## 3             True            2083.333 6954337960046817851BCB2
## 4             True            2875.000 A0393664465886295619C51
## 5             True            9583.333 A180369302188889200689E
## 6             True            8333.333 C3D63702273952547E79520
##   TotalProsperLoans TotalProsperPaymentsBilled OnTimeProsperPayments
## 1                NA                         NA                    NA
## 2                NA                         NA                    NA
## 3                NA                         NA                    NA
## 4                NA                         NA                    NA
## 5                 1                         11                    11
## 6                NA                         NA                    NA
##   ProsperPaymentsLessThanOneMonthLate ProsperPaymentsOneMonthPlusLate
## 1                                  NA                              NA
## 2                                  NA                              NA
## 3                                  NA                              NA
## 4                                  NA                              NA
## 5                                   0                               0
## 6                                  NA                              NA
##   ProsperPrincipalBorrowed ProsperPrincipalOutstanding
## 1                       NA                          NA
## 2                       NA                          NA
## 3                       NA                          NA
## 4                       NA                          NA
## 5                    11000                      9947.9
## 6                       NA                          NA
##   ScorexChangeAtTimeOfListing LoanCurrentDaysDelinquent
## 1                          NA                         0
## 2                          NA                         0
## 3                          NA                         0
## 4                          NA                         0
## 5                          NA                         0
## 6                          NA                         0
##   LoanFirstDefaultedCycleNumber LoanMonthsSinceOrigination LoanNumber
## 1                            NA                         78      19141
## 2                            NA                          0     134815
## 3                            NA                         86       6466
## 4                            NA                         16      77296
## 5                            NA                          6     102670
## 6                            NA                          3     123257
##   LoanOriginalAmount LoanOriginationDate LoanOriginationQuarter
## 1               9425 2007-09-12 00:00:00                Q3 2007
## 2              10000 2014-03-03 00:00:00                Q1 2014
## 3               3001 2007-01-17 00:00:00                Q1 2007
## 4              10000 2012-11-01 00:00:00                Q4 2012
## 5              15000 2013-09-20 00:00:00                Q3 2013
## 6              15000 2013-12-24 00:00:00                Q4 2013
##                 MemberKey MonthlyLoanPayment LP_CustomerPayments
## 1 1F3E3376408759268057EDA             330.43            11396.14
## 2 1D13370546739025387B2F4             318.93                0.00
## 3 5F7033715035555618FA612             123.32             4186.63
## 4 9ADE356069835475068C6D2             321.45             5143.20
## 5 36CE356043264555721F06C             563.97             2819.85
## 6 874A3701157341738DE458F             342.37              679.34
##   LP_CustomerPrincipalPayments LP_InterestandFees LP_ServiceFees
## 1                      9425.00            1971.14        -133.18
## 2                         0.00               0.00           0.00
## 3                      3001.00            1185.63         -24.20
## 4                      4091.09            1052.11        -108.01
## 5                      1563.22            1256.63         -60.27
## 6                       351.89             327.45         -25.33
##   LP_CollectionFees LP_GrossPrincipalLoss LP_NetPrincipalLoss
## 1                 0                     0                   0
## 2                 0                     0                   0
## 3                 0                     0                   0
## 4                 0                     0                   0
## 5                 0                     0                   0
## 6                 0                     0                   0
##   LP_NonPrincipalRecoverypayments PercentFunded Recommendations
## 1                               0             1               0
## 2                               0             1               0
## 3                               0             1               0
## 4                               0             1               0
## 5                               0             1               0
## 6                               0             1               0
##   InvestmentFromFriendsCount InvestmentFromFriendsAmount Investors
## 1                          0                           0       258
## 2                          0                           0         1
## 3                          0                           0        41
## 4                          0                           0       158
## 5                          0                           0        20
## 6                          0                           0         1

Univariate Plots Section

We will be looking at a few variables that relate to both the loan itself (dollar amount, term) and the borrower (credit score, prosper rating) in order to determine what is likely to influence the total amount Prosper is willing to lend a borrower and at what rate.

Borrower Data Exploration: Subsection: Loan Original Amount

We will be examining the LoanOriginalAmount data from the loans dataset to better understand the frequency of loan values provided by Prosper.

head(sort(table(loans$LoanOriginalAmount), decreasing = T), 20)
## 
##  4000 15000 10000  5000  2000  3000 25000 20000  1000  2500  7500  7000 
## 14333 12407 11106  6990  6067  5749  3630  3291  3206  2992  2975  2949 
##  6000  3500  8000 12000  9000 13000  1500  4500 
##  2869  2567  2442  1921  1695  1509  1507  1406
summary(loans$LoanOriginalAmount)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    4000    6500    8337   12000   35000

The table above shows that loans of 4,000 are the most provided by Propser. This value is below the median of 6500 and the Mean of 8337, which suggests there are some large loans that are pulling the mean forward.

The max loan provided by Prosper was 35,000.

qplot(data = loans, x = loans$LoanOriginalAmount, binwidth = 1000)+
  geom_histogram()+
  scale_x_continuous(breaks = seq(0,35000, 2000))+
  ggtitle('Count of Loan Original Amount')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

The histogram above shows a spike at around 3,000- 4,000. This suggests there are a great number of loans provided in this area. Let’s examine further.

qplot(data = loans, x = loans$LoanOriginalAmount, binwidth = 500)+
  geom_histogram()+
  coord_cartesian(xlim = c(0,5000))+
  scale_x_continuous(breaks = seq(0,5000, 1000))+
  ggtitle('Count of Loan Original Amount by Binwidth = 500')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

head(sort(table(loans$LoanOriginalAmount), decreasing = T), 20)
## 
##  4000 15000 10000  5000  2000  3000 25000 20000  1000  2500  7500  7000 
## 14333 12407 11106  6990  6067  5749  3630  3291  3206  2992  2975  2949 
##  6000  3500  8000 12000  9000 13000  1500  4500 
##  2869  2567  2442  1921  1695  1509  1507  1406

Borrower Data Exploration: Subsection: Loan Term

Let’s look at the loan term provided by Prosper to get a sense of what types of loans and duration of loans Prosper gives to their borrowers.

sort(table(loans$Term))
## 
##    12    60    36 
##  1614 24545 87778
table(loans$Term)
## 
##    12    36    60 
##  1614 87778 24545
ggplot(data = loans, aes(x = loans$Term), binwidth = 1)+
  geom_histogram()+
  scale_x_continuous(breaks = seq(0,62,2))+
  ggtitle('Count of loan terms')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

From the table and histogram above, we see that Prosper only gives loans in 12, 36, and 60 month terms. The majority of loans are provided on a 36 month term payment plan.

Borrower Data Exploration: Subsection: Amount Delinquent

We will examine the amount of money that is delinquent per borrower per Prosper loan.

DelinquenciesValues <- subset(loans, loans$AmountDelinquent != 0)
table(DelinquenciesValues$AmountDelinquent)
## 
##      1      2      3      4      5      6      7      8      9     10 
##      7     10      7      6      9      9      5      6      7     30 
##     11     12     13     14     15     16     17     18     19     20 
##      8      9     12     12     34      6     12      6      8     30 
##     21     22     23     24     25     26     27     28     29     30 
##      8     11      8     12     66     14     15     19     15     65 
##     31     32     33     34     35     36     37     38     39     40 
##     22     24     27     20     29     25     22     12     14     43 
##     41     42     43     44     45     46     47     48     49     50 
##     15     22     21     18     26     19     21     24     15     73 
##     51     52     53     54     55     56     57     58     59     60 
##     25     24     23     26     34     21     25     17     17     46 
##     61     62     63     64     65     66     67     68     69     70 
##     17     18     18     22     34     22     32     25     13     29 
##     71     72     73     74     75     76     77     78     79     80 
##     22     17     11     20     56     21     17     23     26     28 
##     81     82     83     84     85     86     87     88     89     90 
##     19     19     15     24     18     19     18     25     13     25 
##     91     92     93     94     95     96     97     98     99    100 
##     13     15     22     22     16     12     20     21     13     67 
##    101    102    103    104    105    106    107    108    109    110 
##     23     19     21     16     25     19     21     17     13     26 
##    111    112    113    114    115    116    117    118    119    120 
##     14     21     19     19     23     20     17     16     15     35 
##    121    122    123    124    125    126    127    128    129    130 
##     13     12     16     13     18     13     11     11     22     31 
##    131    132    133    134    135    136    137    138    139    140 
##     15     20     14     25     21      7      9     19      9     19 
##    141    142    143    144    145    146    147    148    149    150 
##     11     13     14     10     18     12     16     11     13     32 
##    151    152    153    154    155    156    157    158    159    160 
##     14     15     21     11      9     13     11     23      7     15 
##    161    162    163    164    165    166    167    168    169    170 
##     15     14      9     13     10     17     18     12      9     10 
##    171    172    173    174    175    176    177    178    179    180 
##     13     14      9     18     17     11      7     20     14     15 
##    181    182    183    184    185    186    187    188    189    190 
##     12     12     14      9     21      9      8     10     13      9 
##    191    192    193    194    195    196    197    198    199    200 
##     16     13      9     10     10      8     11      9      9     29 
##    201    202    203    204    205    206    207    208    209    210 
##     11     16     12      7      7     15     13      7     14     14 
##    211    212    213    214    215    216    217    218    219    220 
##     10      8     12     18      7      9      9      9      9     18 
##    221    222    223    224    225    226    227    228    229    230 
##      9      6     20     13     15      8     13     20     12     24 
##    231    232    233    234    235    236    237    238    239    240 
##     13      9      9     13      9      9      5      9     10      8 
##    241    242    243    244    245    246    247    248    249    250 
##      9      6      9      8     13     13     10     15     10     20 
##    251    252    253    254    255    256    257    258    259    260 
##     10     11     13     13     12      9     13     15     14     12 
##    261    262    263    264    265    266    267    268    269    270 
##      7      9      9      9     10     13     14      7     19      9 
##    271    272    273    274    275    276    277    278    279    280 
##      7      5     10     10      7     11      7     10     18     15 
##    281    282    283    284    285    286    287    288    289    290 
##     12      4     12     12     14     11      6      9      8     12 
##    291    292    293    294    295    296    297    298    299    300 
##      9      9      8     12     14     14     10     11     10     26 
##    301    302    303    304    305    306    307    308    309    310 
##     10      8      5      8      5     11     10     12      6      8 
##    311    312    313    314    315    316    317    318    319    320 
##      8      4     11      8     10     13      4     10      9     11 
##    321    322    323    324    325    326    327    328    329    330 
##      4      7      4      7      9      5      9      3      3     11 
##    331    332    333    334    335    336    337    338    339    340 
##      6      8      2      4      4     10     10      8      4      8 
##    341    342    343    344    345    346    347    348    349    350 
##      7      7      7      8      2      6      3     10     10     23 
##    351    352    353    354    355    356    357    358    359    360 
##      7     12     12      3      9      8     10     11      6     10 
##    361    362    363    364    365    366    367    368    369    370 
##      6      4     11      5      7      8     10     14      8     15 
##    371    372    373    374    375    376    377    378    379    380 
##      5      9      2      5      8      5      7      9     10     10 
##    381    382    383    384    385    386    387    388    389    390 
##      9     11      9      3      7      8      7      7      6      9 
##    391    392    393    394    395    396    397    398    399    400 
##      6      6      9      4      6      6      5      8      3     16 
##    401    402    403    404    405    406    407    408    409    410 
##     11      8     15      4      7      2      4      7      8      6 
##    411    412    413    414    415    416    417    418    419    420 
##      7      7      6      5      4      9      8      5      6      7 
##    421    422    423    424    425    426    427    428    429    430 
##      4      6      7      6      8      9      6      9      7      5 
##    431    432    433    434    435    436    437    438    439    440 
##      8      4     16      3      3      7      4     10      5      7 
##    441    442    443    444    445    446    447    448    449    450 
##      5      2      4      5      2      9     10      8      4     12 
##    451    452    453    454    455    456    457    458    459    460 
##      5      3      2      7      4      4     10      6      6     15 
##    461    463    464    465    466    467    468    469    470    471 
##      6      8      2      5      4      4      7      5      4      3 
##    472    473    474    475    476    477    478    479    480    481 
##      7      2      7     10      9      5      8      8      6      3 
##    482    483    484    485    486    487    488    489    490    491 
##     10      5      4      5      9      2      4      4     10      6 
##    492    493    494    495    496    497    498    499    500    501 
##      3      3      9     13      6      8      5      6     11      4 
##    502    503    504    505    506    507    508    509    510    511 
##      7      4      6      5      8      2      7      2      8      5 
##    512    513    514    515    516    517    518    519    520    521 
##      7      4      8      7      1      2      9      4      7      5 
##    522    523    524    525    526    527    528    529    530    531 
##      5      3      1     11      8      5      4      5      5      4 
##    532    533    534    535    536    537    538    539    540    541 
##      6      6     10      8     10      2      5      5      5      6 
##    542    543    544    545    546    547    548    549    550    551 
##      5      8      2      5      6      6      7      6      7      4 
##    552    553    554    555    556    557    558    559    560    561 
##      7      7      3      4      3      4      2      4      8      7 
##    562    563    564    565    566    567    568    569    570    571 
##      2      3      2      3      7      7      6      6      8      5 
##    572    573    574    575    576    577    578    579    580    581 
##      6      3      3      3      4      8      4      6      3      2 
##    582    583    584    585    586    587    588    589    590    591 
##      4      5      6      3      4      8      2      6     11      8 
##    592    593    594    595    596    597    598    599    600    601 
##      3      2      1      7      8      7      5      4     17      3 
##    602    603    604    605    606    607    608    609    610    611 
##      3      8      2      4      2      3      5      8      6      7 
##    612    613    614    615    616    617    618    619    620    621 
##      2      6      5      4      4      4      7     10      7      2 
##    622    623    624    625    626    627    628    630    631    632 
##      3      5      6      2      4      4      3     10      3      5 
##    633    634    635    636    637    638    639    640    641    642 
##      9      2      5      2      7      5      3      5      7      5 
##    643    644    645    646    647    648    649    650    651    652 
##      4     10      4      3      5      9      2     12      2      3 
##    653    654    655    656    657    658    659    660    661    662 
##      3      6      4      8      6      5      5      7      5      6 
##    663    664    665    666    667    668    669    670    671    672 
##      3      7      2     11      4      4      3      2     11      5 
##    673    674    675    676    677    678    679    680    681    682 
##      4      3      5      3      7      5      3      3      2      2 
##    683    684    686    687    688    689    690    691    692    693 
##      5      2     10      2      3      6      3      6      8      5 
##    694    695    696    697    698    699    700    701    702    703 
##      9      4      2      1      6      1     10      2      2      5 
##    704    705    706    707    708    709    710    711    712    713 
##      3      1      7      6      5      2      6      5      4      5 
##    714    715    716    717    718    719    720    721    722    723 
##      2      6      3      1      2      4      4      4      4      5 
##    724    725    726    727    728    729    730    731    732    733 
##      3      7      9      3      4      2      2      4      2      3 
##    734    735    736    737    738    739    740    741    742    743 
##      1      4      6      4      1      5      5      1      2      2 
##    744    745    746    747    748    749    750    751    752    753 
##      3      1      2      1      5      1     10      8      6      5 
##    754    755    756    757    758    759    760    761    762    763 
##      5      7      2      4      6      2      3      4      4      2 
##    764    765    766    767    768    769    770    771    772    773 
##      4      7      3      4      2      2      7      3      7      5 
##    774    775    776    777    778    779    780    781    782    783 
##      3      6      5      4      2      2      3      1      3      4 
##    784    785    786    787    788    789    790    791    793    795 
##      5      3      1      5      1      3      2      8      2      3 
##    796    797    798    799    800    801    802    803    804    805 
##      2      2      1      2      7      1      2      2      8      7 
##    806    807    808    809    810    811    812    813    814    815 
##      3      2      2      5      5      1      1      1      7      5 
##    816    817    818    819    820    821    822    823    824    825 
##      2      2      3      2      4      2      5      3      2      1 
##    826    827    828    829    830    831    832    833    834    835 
##      1      1      1      5      4      1      4      1      4      4 
##    836    837    838    839    840    841    842    843    844    845 
##      2      3      3      3      5      3      7      1      2      7 
##    846    847    848    849    850    851    852    853    854    855 
##      4      1      3      3      6      4      2      3      2      7 
##    856    857    858    859    860    861    862    863    864    865 
##      3      2      2      3      1      5      6      1      6      3 
##    866    867    868    869    870    872    873    874    875    876 
##      2      1      2      4      6      4      3      3      5      5 
##    877    878    879    880    881    882    883    884    885    886 
##      2      1      3      5      2      3      3      4      3      5 
##    887    888    889    890    891    892    893    894    895    896 
##      8      2      1      6      3      2      4      2      6      3 
##    897    898    899    900    902    903    904    905    906    907 
##      3      5      1      4      4      2      3      4      2      2 
##    908    909    910    912    913    914    915    916    917    918 
##      1      2      1      5      2      1      2      2      7      4 
##    919    920    921    922    923    924    925    926    927    928 
##      3      1      2      3      2      3      2      3      4      3 
##    929    930    931    932    933    934    935    936    937    938 
##      1      2      7      6      2      5      1      5      2      4 
##    939    940    941    942    943    944    945    946    947    948 
##      2      2      3      2      2      1      2      4      3      2 
##    949    951    952    953    954    955    957    959    960    961 
##      4      3      3      1      2      2      2      5      5      2 
##    962    963    965    966    969    970    971    972    973    974 
##      2      1      1      1      4      1      4      3      1      1 
##    975    976    977    978    979    980    982    983    984    985 
##      2      7      3      2      1      3      2      2      2      3 
##    986    987    988    989    990    991    992    993    994    995 
##      1      1      2      2      1      1      5      2      4      4 
##    996    997    998    999   1000   1001   1002   1003   1004   1005 
##      4      3      5      1      2      4      4      5      4      2 
##   1006   1007   1008   1009   1010   1011   1012   1013   1014   1015 
##      3      1      3      2      6      7      3      3      3      1 
##   1016   1017   1018   1019   1020   1021   1022   1023   1024   1025 
##      4      2      4      1      1      3      1      3      4      2 
##   1026   1027   1028   1029   1030   1031   1032   1033   1034   1035 
##      6      2      3      3      1      2      3      1      3      3 
##   1037   1038   1039   1040   1042   1043   1044   1046   1047   1048 
##      2      1      4      1      2      1      3      1      3      2 
##   1049   1050   1051   1052   1053   1054   1055   1056   1057   1058 
##      2      3      1      2      1      3      2      5      2      3 
##   1059   1060   1061   1062   1063   1064   1066   1067   1068   1069 
##      2      3      3      3      1      4      6      4      2      2 
##   1070   1071   1072   1073   1074   1075   1077   1078   1079   1080 
##      3      4      3      4      4      2      2      4      1      2 
##   1081   1082   1083   1084   1086   1087   1088   1089   1090   1091 
##      1      3      1      7      1      3      2      1      5      4 
##   1092   1093   1094   1095   1096   1097   1098   1099   1100   1101 
##      2      1      6      6      3      2      2      3      2      2 
##   1102   1103   1104   1105   1106   1107   1108   1109   1110   1111 
##      5      5      3      6      1      4      5      2      5      2 
##   1112   1113   1114   1115   1116   1117   1118   1119   1120   1121 
##      5      1      1      3      3      2      2      6      1      4 
##   1122   1123   1124   1125   1126   1127   1129   1130   1132   1133 
##      3      1      3      2      6      4      3      4      3      3 
##   1134   1135   1136   1137   1138   1139   1140   1141   1142   1143 
##      3      1      3      4      2      2      6      1      5      2 
##   1144   1145   1146   1147   1148   1149   1150   1151   1152   1153 
##      2      1      3      1      4      1      2      1      2      1 
##   1154   1155   1156   1157   1159   1160   1161   1162   1164   1165 
##      2      8      5      1      2      3      3      3      4      3 
##   1166   1167   1168   1169   1170   1171   1172   1173   1174   1175 
##      4      1      1      1      2      4      5      2      5      5 
##   1176   1177   1178   1179   1180   1181   1183   1184   1185   1186 
##      3      3      5      3      5      5      4      1      1      3 
##   1187   1188   1189   1190   1192   1195   1196   1197   1198   1199 
##      2      4      2      1      5      1      2      2      1      3 
##   1200   1201   1202   1203   1205   1206   1207   1208   1209   1210 
##      2      3      3      1      4      1      7      1      1      3 
##   1211   1212   1213   1214   1215   1217   1218   1219   1220   1223 
##      3      7      1      4      3      3      3      4      3      1 
##   1224   1225   1226   1227   1228   1229   1231   1232   1233   1234 
##      3      3      1      6      3      5      1      2      3      7 
##   1235   1236   1238   1241   1242   1243   1244   1245   1246   1247 
##      4      2      4      2      3      2      2      4      2      5 
##   1248   1249   1250   1251   1252   1253   1254   1255   1257   1259 
##      1      1      6      2      3      2      1      3      2      3 
##   1260   1261   1262   1264   1265   1266   1267   1268   1269   1270 
##      5      4      3      3      2      2      4      1      1      6 
##   1271   1272   1273   1274   1275   1276   1277   1278   1279   1280 
##      2      2      1      2      3      1      1      2      2      1 
##   1281   1282   1283   1285   1286   1287   1288   1289   1290   1291 
##      3      3      4      3      2      4      1      4      1      1 
##   1292   1293   1294   1297   1299   1300   1301   1302   1303   1304 
##      2      5      1      2      1      3      2      4      2      2 
##   1305   1306   1307   1308   1309   1310   1311   1312   1313   1314 
##      4      1      3      3      1      2      2      2      3      4 
##   1315   1317   1318   1320   1321   1322   1323   1324   1325   1327 
##      2      1      2      2      1      4      1      1      2      3 
##   1328   1329   1331   1332   1333   1334   1335   1336   1337   1338 
##      1      2      2      1      6      2      4      1      1      1 
##   1339   1340   1341   1342   1343   1344   1345   1346   1347   1348 
##      2      2      1      2      2      6      1      5      2      3 
##   1349   1350   1351   1352   1353   1354   1355   1356   1358   1359 
##      2      2      1      1      2      3      3      3      5      2 
##   1360   1361   1363   1364   1365   1366   1368   1370   1372   1374 
##      2      2      2      2      3      2      3      6      2      4 
##   1375   1377   1378   1379   1380   1381   1382   1383   1384   1386 
##      1      1      3      1      2      6      1      1      3      3 
##   1387   1388   1390   1391   1392   1393   1395   1396   1397   1398 
##      2      2      2      2      1      1      2      2      1      2 
##   1399   1400   1401   1402   1404   1405   1406   1407   1408   1409 
##      3      1      2      1      2      3      2      1      1      3 
##   1410   1411   1412   1413   1414   1415   1416   1417   1418   1419 
##      1      2      2      3      1      4      2      1      1      2 
##   1421   1423   1424   1425   1426   1427   1429   1430   1431   1432 
##      2      3      2      6      4      3      1      1      5      4 
##   1433   1434   1435   1436   1437   1440   1441   1442   1444   1445 
##      2      3      1      2      1      2      2      3      2      2 
##   1446   1447   1448   1449   1450   1451   1454   1455   1458   1459 
##      1      4      1      2      3      2      3      1      2      4 
##   1460   1461   1462   1463   1464   1465   1466   1467   1468   1470 
##      1      2      3      3      6      1      5      2      1      1 
##   1471   1472   1473   1474   1475   1476   1477   1479   1480   1481 
##      1      5      3      1      1      2      2      2      6      4 
##   1483   1484   1485   1486   1487   1488   1490   1491   1493   1494 
##      1      3      1      1      1      3      2      2      3      1 
##   1495   1496   1497   1498   1499   1500   1501   1503   1504   1505 
##      4      3      1      2      2      8      3      1      2      3 
##   1509   1510   1511   1512   1513   1514   1515   1516   1517   1518 
##      3      1      2      3      3      1      1      2      2      5 
##   1520   1521   1522   1523   1525   1526   1528   1529   1530   1531 
##      1      1      3      4      1      1      1      1      2      1 
##   1532   1533   1534   1535   1536   1537   1538   1539   1540   1541 
##      2      2      1      2      4      1      2      1      1      2 
##   1542   1544   1546   1547   1548   1549   1550   1551   1552   1553 
##      2      2      1      2      1      3      2      2      1      3 
##   1554   1555   1556   1557   1558   1560   1561   1562   1563   1564 
##      1      1      3      2      4      2      1      1      2      3 
##   1565   1568   1569   1570   1571   1572   1573   1574   1575   1576 
##      3      4      5      4      1      1      2      2      2      2 
##   1577   1578   1582   1583   1584   1585   1586   1587   1588   1589 
##      1      3      2      6      2      2      1      1      2      2 
##   1590   1592   1593   1594   1596   1597   1598   1599   1600   1601 
##      2      1      4      1      2      5      2      3      3      1 
##   1602   1603   1605   1606   1607   1608   1609   1611   1612   1613 
##      4      4      1      2      1      1      2      2      2      2 
##   1614   1615   1617   1619   1620   1622   1623   1624   1625   1627 
##      1      2      2      4      6      1      5      1      2      1 
##   1628   1629   1630   1631   1632   1633   1634   1635   1636   1638 
##      1      1      3      2      4      1      4      1      3      2 
##   1640   1641   1642   1643   1644   1645   1646   1647   1648   1650 
##      4      2      2      1      1      1      1      1      2      5 
##   1651   1652   1653   1655   1656   1657   1659   1660   1661   1662 
##      1      1      2      5      2      3      1      5      1      2 
##   1663   1665   1666   1667   1668   1670   1671   1673   1674   1675 
##      1      2      2      3      2      4      2      3      3      2 
##   1676   1678   1679   1680   1681   1684   1685   1687   1688   1689 
##      1      4      1      3      2      2      1      2      1      3 
##   1690   1694   1695   1697   1698   1699   1700   1701   1702   1703 
##      2      1      3      1      2      1      1      1      1      2 
##   1704   1705   1706   1707   1708   1709   1711   1712   1714   1716 
##      4      1      3      1      1      1      1      1      2      3 
##   1717   1718   1719   1720   1721   1723   1724   1725   1726   1727 
##      1      1      1      2      2      2      3      1      3      2 
##   1728   1729   1730   1731   1733   1734   1735   1736   1737   1738 
##      2      2      1      1      1      1      1      1      1      4 
##   1739   1740   1741   1742   1743   1744   1745   1746   1747   1749 
##      1      1      2      2      1      1      3      1      2      2 
##   1750   1754   1756   1758   1760   1761   1762   1764   1765   1766 
##      2      2      1      4      2      1      1      2      1      3 
##   1767   1768   1769   1770   1771   1773   1774   1775   1776   1778 
##      1      1      1      1      1      2      2      6      1      2 
##   1779   1780   1781   1782   1783   1784   1785   1786   1787   1790 
##      1      5      4      1      2      1      1      1      1      1 
##   1791   1792   1794   1795   1796   1797   1799   1800   1801   1802 
##      1      4      2      4      2      1      1      5      2      2 
##   1803   1804   1805   1806   1809   1810   1811   1812   1813   1814 
##      1      1      4      1      1      2      2      3      3      1 
##   1816   1817   1818   1820   1821   1822   1823   1824   1825   1826 
##      4      2      2      1      2      4      1      5      4      2 
##   1827   1828   1829   1830   1831   1832   1834   1835   1836   1837 
##      2      2      3      1      1      1      1      1      5      2 
##   1838   1839   1840   1841   1842   1844   1845   1846   1847   1848 
##      2      3      3      1      1      1      1      1      2      1 
##   1849   1850   1851   1852   1853   1854   1856   1860   1861   1862 
##      1      1      1      2      2      2      1      2      2      4 
##   1863   1864   1865   1866   1867   1868   1870   1872   1873   1874 
##      1      1      1      1      1      2      2      2      3      2 
##   1875   1877   1878   1879   1881   1882   1883   1885   1886   1887 
##      2      3      1      3      3      2      1      4      1      1 
##   1889   1890   1891   1892   1895   1896   1898   1899   1901   1902 
##      3      2      4      2      3      2      1      3      3      1 
##   1903   1904   1905   1906   1907   1908   1909   1911   1913   1914 
##      2      2      1      1      1      3      1      1      1      1 
##   1915   1916   1917   1918   1919   1920   1924   1925   1926   1929 
##      1      1      1      1      2      2      3      1      2      1 
##   1930   1931   1932   1933   1934   1935   1937   1938   1939   1941 
##      2      1      2      3      2      3      1      2      1      1 
##   1942   1943   1944   1946   1947   1949   1951   1952   1953   1954 
##      3      1      2      2      3      4      2      1      1      2 
##   1955   1956   1957   1958   1960   1961   1963   1965   1966   1969 
##      1      1      1      1      4      3      1      1      2      1 
##   1973   1974   1975   1977   1979   1980   1981   1982   1983   1985 
##      1      1      1      1      1      2      3      1      1      2 
##   1986   1989   1990   1991   1993   1998   2001   2002   2003   2006 
##      1      1      1      3      1      1      2      2      3      1 
##   2007   2008   2011   2012   2013   2015   2016   2017   2018   2021 
##      5      3      1      2      2      5      2      3      1      2 
##   2022   2023   2024   2025   2026   2027   2028   2029   2030   2031 
##      2      1      1      2      1      3      2      2      1      2 
##   2032   2033   2034   2036   2037   2038   2040   2041   2042   2043 
##      1      1      3      1      1      3      2      2      1      3 
##   2044   2045   2046   2047   2049   2050   2051   2052   2054   2055 
##      1      1      2      5      2      3      4      1      1      1 
##   2056   2057   2060   2061   2064   2065   2066   2067   2069   2071 
##      2      1      3      1      1      2      1      2      1      1 
##   2072   2073   2074   2075   2076   2078   2079   2081   2082   2083 
##      1      3      2      1      2      2      2      4      1      2 
##   2084   2086   2090   2091   2092   2099   2100   2101   2102   2104 
##      3      1      2      2      2      2      3      2      1      2 
##   2107   2110   2111   2113   2114   2116   2117   2118   2119   2120 
##      1      1      2      2      3      1      2      1      1      1 
##   2121   2122   2123   2124   2125   2126   2127   2129   2130   2131 
##      2      3      1      1      1      1      3      1      1      1 
##   2133   2135   2137   2138   2141   2142   2143   2145   2146   2147 
##      3      1      2      1      2      1      1      1      1      1 
##   2148   2150   2152   2153   2154   2156   2157   2159   2160   2161 
##      2      1      1      2      2      1      1      3      1      2 
##   2164   2165   2166   2169   2170   2171   2174   2175   2177   2178 
##      2      1      1      1      1      1      2      2      1      2 
##   2180   2181   2182   2184   2185   2186   2188   2189   2190   2191 
##      1      1      1      1      1      2      1      2      1      2 
##   2193   2194   2195   2197   2198   2200   2202   2203   2205   2206 
##      2      1      1      1      1      1      3      1      1      2 
##   2207   2208   2211   2212   2213   2214   2215   2216   2218   2219 
##      1      2      1      3      2      1      1      2      1      2 
##   2220   2221   2222   2224   2225   2226   2227   2228   2229   2230 
##      1      2      1      2      1      1      3      2      1      1 
##   2233   2237   2238   2240   2243   2244   2249   2250   2251   2252 
##      1      2      2      1      1      2      1      3      1      2 
##   2253   2254   2255   2260   2261   2262   2264   2268   2269   2270 
##      1      2      2      1      2      2      2      2      1      1 
##   2271   2272   2273   2274   2275   2278   2279   2281   2282   2283 
##      1      1      2      2      2      2      4      1      1      2 
##   2285   2286   2287   2288   2289   2290   2291   2292   2293   2294 
##      3      2      1      2      3      2      2      1      1      1 
##   2295   2296   2298   2300   2301   2302   2303   2304   2305   2306 
##      2      2      4      1      1      1      2      2      2      1 
##   2307   2308   2309   2310   2311   2313   2316   2317   2318   2320 
##      1      3      1      1      1      1      3      1      1      2 
##   2321   2322   2325   2326   2328   2329   2331   2334   2336   2337 
##      1      3      1      1      1      2      1      2      2      3 
##   2340   2341   2343   2345   2346   2347   2348   2349   2352   2353 
##      1      1      2      2      1      2      1      1      2      4 
##   2354   2356   2358   2360   2361   2362   2363   2364   2366   2367 
##      2      1      2      3      2      1      1      1      2      1 
##   2368   2369   2370   2371   2372   2373   2374   2376   2377   2381 
##      2      3      2      2      1      2      1      1      1      1 
##   2383   2384   2385   2386   2387   2389   2390   2391   2392   2394 
##      3      1      3      1      2      1      1      3      1      2 
##   2396   2397   2398   2399   2400   2403   2404   2405   2410   2411 
##      2      2      1      1      1      2      3      4      4      1 
##   2415   2416   2419   2420   2421   2422   2424   2426   2428   2429 
##      1      4      1      1      1      3      1      1      2      1 
##   2430   2431   2432   2433   2434   2435   2436   2438   2441   2442 
##      1      2      1      1      3      1      1      1      2      1 
##   2444   2445   2447   2450   2451   2453   2456   2457   2458   2459 
##      1      2      1      1      1      1      1      2      1      3 
##   2460   2463   2464   2466   2467   2468   2469   2471   2476   2478 
##      1      2      2      1      2      1      2      1      2      3 
##   2479   2480   2481   2482   2483   2485   2488   2489   2491   2495 
##      1      3      1      1      1      2      1      4      1      1 
##   2497   2499   2500   2502   2504   2505   2506   2508   2509   2511 
##      1      1      3      1      1      1      3      1      1      1 
##   2512   2513   2514   2515   2516   2518   2523   2524   2525   2526 
##      2      1      1      1      1      2      1      2      1      1 
##   2527   2530   2531   2532   2533   2534   2535   2536   2538   2539 
##      1      3      1      2      1      1      4      1      1      1 
##   2540   2541   2542   2543   2544   2546   2548   2549   2550   2553 
##      2      1      2      1      1      2      1      1      4      3 
##   2554   2555   2556   2557   2558   2559   2561   2562   2564   2565 
##      2      2      1      3      2      1      1      2      1      3 
##   2566   2567   2569   2570   2571   2572   2573   2574   2575   2578 
##      1      2      1      1      3      3      3      1      1      2 
##   2579   2580   2582   2583   2584   2586   2587   2588   2589   2590 
##      1      3      1      2      3      1      1      1      1      2 
##   2591   2593   2595   2597   2598   2600   2601   2602   2603   2605 
##      3      2      1      3      3      4      3      2      1      2 
##   2606   2607   2608   2609   2611   2612   2613   2617   2618   2620 
##      1      1      1      1      1      1      1      1      1      1 
##   2621   2624   2628   2629   2630   2631   2632   2633   2634   2635 
##      2      1      2      1      1      2      1      3      1      2 
##   2638   2640   2641   2643   2644   2646   2647   2648   2650   2651 
##      1      1      1      1      1      1      2      1      1      1 
##   2653   2654   2656   2658   2659   2660   2661   2662   2664   2666 
##      1      2      2      2      1      1      2      1      1      1 
##   2667   2670   2677   2678   2679   2681   2682   2683   2684   2685 
##      1      1      1      1      2      1      2      1      4      3 
##   2686   2687   2691   2695   2696   2697   2699   2700   2701   2703 
##      1      4      2      1      3      2      1      2      1      1 
##   2705   2706   2707   2708   2709   2710   2711   2712   2713   2715 
##      3      1      1      1      1      1      1      1      2      2 
##   2717   2719   2720   2723   2724   2726   2727   2728   2729   2730 
##      1      1      1      3      1      1      1      2      1      2 
##   2732   2735   2737   2739   2742   2744   2746   2747   2750   2751 
##      2      2      2      1      3      2      1      2      3      1 
##   2753   2754   2755   2756   2757   2758   2759   2765   2766   2767 
##      1      1      2      1      4      2      3      2      2      2 
##   2768   2769   2770   2772   2773   2774   2775   2776   2777   2778 
##      1      1      1      2      1      1      1      2      1      1 
##   2779   2782   2783   2784   2786   2787   2788   2790   2791   2792 
##      2      2      1      2      3      1      1      1      1      3 
##   2794   2795   2796   2797   2798   2800   2801   2802   2804   2806 
##      1      1      1      1      1      2      3      1      1      1 
##   2807   2808   2809   2811   2812   2814   2815   2817   2818   2819 
##      1      2      3      1      1      1      1      4      1      1 
##   2820   2821   2822   2823   2824   2825   2826   2827   2828   2829 
##      2      2      3      1      1      1      2      3      5      2 
##   2831   2832   2835   2836   2839   2840   2841   2844   2845   2846 
##      1      1      2      1      1      1      2      2      2      1 
##   2849   2850   2851   2852   2853   2855   2856   2858   2859   2860 
##      3      1      1      2      3      1      1      1      1      2 
##   2861   2862   2863   2866   2868   2869   2870   2874   2876   2877 
##      1      2      1      1      1      1      1      3      3      5 
##   2880   2881   2883   2884   2885   2886   2888   2892   2896   2897 
##      2      1      1      1      3      1      1      1      1      2 
##   2898   2900   2901   2903   2904   2909   2910   2914   2915   2917 
##      1      2      1      2      1      1      1      1      2      2 
##   2919   2921   2922   2923   2924   2926   2927   2931   2933   2936 
##      1      1      1      2      2      3      1      1      1      1 
##   2938   2940   2942   2947   2948   2949   2950   2951   2952   2953 
##      2      1      1      1      1      1      1      3      2      1 
##   2954   2956   2957   2961   2963   2964   2965   2969   2970   2971 
##      1      1      1      1      1      1      1      2      1      1 
##   2974   2975   2980   2982   2983   2984   2986   2987   2988   2989 
##      2      2      2      1      1      1      1      1      2      1 
##   2990   2992   2993   2994   2996   2997   2998   3000   3001   3002 
##      1      1      3      1      2      2      1      2      1      1 
##   3003   3004   3005   3006   3008   3010   3012   3013   3014   3015 
##      1      1      1      1      1      1      1      1      1      2 
##   3016   3021   3025   3026   3028   3030   3034   3035   3036   3037 
##      2      1      2      2      2      1      1      1      2      2 
##   3038   3040   3042   3044   3045   3046   3048   3054   3055   3056 
##      1      1      1      2      2      1      1      2      1      2 
##   3057   3058   3060   3061   3062   3064   3066   3068   3070   3071 
##      1      1      1      2      1      1      2      1      2      2 
##   3072   3073   3077   3078   3079   3080   3084   3085   3090   3093 
##      1      1      1      1      3      1      2      1      1      2 
##   3096   3098   3099   3100   3103   3105   3109   3110   3111   3114 
##      2      1      1      2      2      3      3      1      3      3 
##   3117   3118   3120   3121   3125   3126   3127   3128   3130   3132 
##      1      2      1      1      2      1      3      1      2      3 
##   3134   3135   3136   3137   3138   3140   3145   3147   3150   3151 
##      1      1      1      2      2      2      2      1      2      1 
##   3152   3157   3158   3161   3162   3163   3164   3165   3167   3168 
##      1      1      1      1      1      1      1      1      2      1 
##   3170   3172   3175   3178   3180   3181   3183   3184   3186   3187 
##      1      1      1      1      1      1      1      1      2      1 
##   3188   3191   3192   3193   3194   3197   3198   3202   3204   3206 
##      4      1      1      2      1      2      1      1      1      1 
##   3207   3208   3212   3214   3215   3217   3219   3222   3223   3224 
##      2      1      1      3      2      1      1      3      1      1 
##   3225   3226   3227   3231   3232   3233   3235   3236   3237   3238 
##      1      2      1      1      2      1      1      3      1      2 
##   3239   3240   3241   3245   3246   3249   3251   3253   3254   3256 
##      1      1      1      1      1      1      1      1      1      1 
##   3258   3259   3260   3261   3263   3265   3268   3269   3272   3273 
##      2      1      1      2      1      1      1      1      1      2 
##   3277   3278   3279   3281   3282   3283   3284   3285   3287   3288 
##      1      2      2      1      1      1      2      2      1      2 
##   3289   3291   3294   3295   3296   3298   3301   3303   3304   3306 
##      1      1      1      1      2      1      1      1      1      1 
##   3307   3308   3311   3313   3314   3317   3318   3319   3321   3322 
##      1      1      1      1      1      1      2      1      1      1 
##   3323   3328   3329   3330   3331   3332   3336   3337   3342   3347 
##      2      1      1      3      1      1      1      2      1      1 
##   3349   3350   3352   3356   3358   3359   3360   3365   3368   3369 
##      1      1      1      2      1      2      3      1      2      1 
##   3370   3375   3378   3379   3380   3382   3383   3384   3386   3388 
##      1      2      1      2      1      1      2      2      1      1 
##   3391   3394   3395   3396   3399   3400   3401   3402   3403   3404 
##      1      2      2      1      1      2      1      1      1      1 
##   3405   3407   3408   3411   3414   3416   3419   3420   3423   3424 
##      3      1      1      1      1      1      2      3      1      2 
##   3425   3427   3428   3430   3432   3433   3435   3436   3437   3440 
##      1      2      1      1      3      2      2      1      1      2 
##   3441   3442   3443   3444   3445   3450   3452   3454   3455   3456 
##      3      1      1      2      3      3      1      1      1      2 
##   3459   3460   3461   3464   3466   3467   3468   3471   3472   3473 
##      1      1      1      2      1      2      1      2      1      1 
##   3474   3475   3477   3478   3479   3481   3482   3483   3484   3485 
##      1      2      2      2      3      1      1      2      1      1 
##   3489   3494   3495   3496   3499   3500   3507   3511   3516   3517 
##      1      1      1      1      2      2      2      1      1      1 
##   3520   3522   3525   3527   3528   3529   3531   3534   3535   3536 
##      1      2      1      1      1      1      1      2      1      3 
##   3537   3539   3541   3542   3543   3544   3547   3550   3551   3552 
##      1      2      2      1      3      1      1      3      1      1 
##   3553   3555   3557   3560   3561   3562   3564   3571   3572   3575 
##      2      1      1      2      1      1      1      2      4      3 
##   3576   3577   3578   3580   3581   3582   3585   3586   3590   3594 
##      1      1      1      1      1      1      1      1      2      1 
##   3597   3599   3600   3603   3604   3606   3608   3609   3610   3613 
##      2      1      2      3      1      1      2      1      2      1 
##   3614   3615   3617   3619   3622   3623   3626   3627   3631   3632 
##      1      1      1      1      1      2      3      2      1      1 
##   3633   3634   3637   3638   3639   3640   3642   3644   3648   3650 
##      2      1      1      1      1      1      1      1      1      2 
##   3651   3658   3659   3660   3661   3663   3665   3666   3668   3670 
##      3      1      1      1      1      1      2      1      1      2 
##   3671   3672   3674   3676   3677   3678   3681   3682   3683   3686 
##      1      2      2      1      1      1      1      1      1      1 
##   3687   3688   3690   3691   3697   3698   3699   3700   3702   3703 
##      1      1      1      1      1      1      1      2      3      2 
##   3705   3706   3707   3708   3712   3713   3714   3715   3716   3717 
##      1      1      1      1      1      1      2      2      1      2 
##   3720   3724   3725   3726   3730   3731   3733   3735   3738   3742 
##      3      1      2      1      1      2      1      1      1      2 
##   3745   3746   3751   3754   3756   3758   3764   3766   3769   3771 
##      1      1      1      3      1      2      1      1      5      1 
##   3773   3776   3780   3784   3786   3787   3788   3791   3797   3801 
##      1      1      2      1      2      1      2      1      1      1 
##   3804   3806   3809   3811   3813   3814   3815   3818   3820   3821 
##      1      1      2      2      2      2      1      2      1      1 
##   3822   3825   3830   3831   3832   3842   3843   3846   3847   3849 
##      1      1      1      1      1      1      1      1      1      1 
##   3850   3851   3853   3860   3861   3862   3867   3868   3870   3871 
##      1      1      1      1      1      2      3      1      1      1 
##   3873   3875   3882   3886   3887   3888   3889   3890   3893   3894 
##      2      2      1      1      1      1      1      1      1      1 
##   3896   3900   3901   3904   3906   3907   3908   3913   3914   3918 
##      1      1      1      1      1      2      2      2      2      1 
##   3919   3920   3921   3926   3929   3930   3931   3932   3933   3935 
##      1      2      2      1      3      1      1      1      1      1 
##   3936   3937   3938   3939   3940   3941   3942   3947   3948   3949 
##      2      1      1      1      1      2      1      1      2      1 
##   3952   3953   3954   3956   3957   3960   3965   3966   3969   3971 
##      2      1      1      3      1      1      1      1      2      1 
##   3976   3979   3980   3985   3986   3987   3990   3991   3992   3995 
##      3      1      1      1      1      1      1      2      1      1 
##   3996   4000   4001   4002   4006   4007   4008   4009   4010   4012 
##      2      2      1      1      1      1      1      1      1      3 
##   4014   4016   4019   4022   4023   4024   4025   4026   4027   4033 
##      1      1      1      2      1      1      1      1      2      1 
##   4034   4036   4040   4041   4042   4044   4047   4049   4050   4051 
##      1      3      2      2      1      1      2      1      1      2 
##   4052   4054   4055   4056   4060   4063   4067   4071   4074   4075 
##      1      2      1      2      2      1      1      1      1      1 
##   4076   4077   4079   4080   4081   4082   4084   4086   4090   4091 
##      1      1      1      2      1      1      2      1      1      1 
##   4096   4097   4098   4106   4107   4109   4113   4117   4119   4124 
##      1      2      1      2      1      1      1      1      1      1 
##   4125   4127   4128   4129   4130   4131   4135   4138   4145   4147 
##      1      2      3      1      1      1      1      1      3      1 
##   4148   4149   4150   4153   4154   4157   4164   4166   4167   4168 
##      1      3      1      1      2      1      2      1      1      1 
##   4171   4172   4173   4174   4176   4177   4179   4180   4182   4185 
##      4      2      4      2      1      1      1      1      1      2 
##   4192   4195   4196   4203   4205   4209   4210   4212   4214   4215 
##      1      1      2      2      3      2      1      1      2      1 
##   4217   4219   4223   4229   4231   4232   4235   4236   4238   4239 
##      1      2      2      3      1      1      2      1      1      1 
##   4240   4245   4250   4251   4255   4256   4257   4258   4259   4261 
##      2      1      1      2      2      1      2      1      1      2 
##   4262   4263   4265   4266   4267   4269   4270   4271   4273   4280 
##      1      1      1      1      2      2      1      1      3      1 
##   4286   4288   4289   4291   4292   4295   4297   4298   4299   4300 
##      1      2      1      1      1      1      1      1      1      1 
##   4301   4306   4310   4311   4313   4317   4318   4319   4320   4321 
##      1      2      3      1      1      2      1      1      1      1 
##   4322   4323   4325   4326   4327   4328   4329   4331   4335   4336 
##      1      3      1      1      1      2      1      1      1      1 
##   4339   4340   4341   4348   4351   4356   4357   4363   4365   4369 
##      2      2      1      1      1      5      2      1      1      1 
##   4371   4375   4376   4378   4382   4386   4388   4391   4393   4398 
##      1      1      1      1      1      1      1      2      1      1 
##   4400   4403   4407   4409   4410   4411   4413   4414   4420   4422 
##      1      1      1      2      2      2      1      1      2      1 
##   4423   4425   4429   4430   4431   4432   4434   4435   4437   4439 
##      2      3      3      2      1      1      1      1      1      1 
##   4440   4441   4442   4443   4444   4445   4451   4453   4457   4458 
##      1      1      1      1      2      1      2      1      1      1 
##   4459   4461   4462   4465   4468   4469   4477   4481   4485   4486 
##      1      2      1      1      1      1      1      1      2      2 
##   4490   4495   4496   4497   4498   4500   4501   4502   4503   4508 
##      1      2      1      2      2      1      2      1      1      1 
##   4511   4513   4514   4518   4519   4520   4522   4523   4529   4535 
##      1      1      1      1      1      1      1      1      1      1 
##   4540   4545   4551   4554   4556   4558   4560   4562   4563   4566 
##      2      1      1      3      1      1      1      1      1      1 
##   4572   4579   4580   4581   4584   4586   4587   4591   4594   4595 
##      1      3      1      2      3      1      1      1      2      1 
##   4597   4600   4603   4604   4605   4608   4609   4611   4612   4618 
##      1      1      1      3      1      2      2      1      1      1 
##   4621   4622   4624   4627   4630   4632   4633   4634   4636   4643 
##      1      1      1      2      2      1      1      1      2      1 
##   4649   4650   4651   4655   4659   4661   4663   4666   4667   4671 
##      1      4      2      1      1      1      1      1      3      1 
##   4672   4675   4679   4681   4682   4685   4686   4693   4697   4700 
##      1      1      2      1      1      1      2      1      1      1 
##   4702   4703   4705   4706   4708   4709   4712   4714   4715   4716 
##      1      1      1      1      1      2      1      1      1      1 
##   4717   4719   4720   4721   4723   4725   4727   4728   4730   4733 
##      1      1      1      1      1      1      1      1      1      1 
##   4740   4742   4743   4745   4747   4749   4750   4751   4756   4757 
##      1      1      2      1      1      1      1      2      1      3 
##   4762   4763   4766   4768   4770   4773   4776   4777   4783   4787 
##      1      1      1      1      1      2      1      2      1      2 
##   4789   4792   4793   4794   4797   4803   4804   4806   4814   4818 
##      1      1      1      1      1      1      1      1      1      1 
##   4819   4820   4823   4827   4831   4832   4837   4840   4841   4842 
##      1      2      1      2      1      2      1      1      1      1 
##   4843   4846   4847   4848   4850   4855   4858   4859   4860   4861 
##      1      2      1      1      2      1      1      1      1      1 
##   4863   4871   4874   4878   4882   4885   4887   4890   4894   4895 
##      1      1      1      1      2      1      1      2      2      1 
##   4897   4901   4904   4905   4908   4916   4917   4921   4930   4931 
##      1      1      1      1      2      1      1      1      1      1 
##   4936   4940   4941   4943   4944   4946   4951   4955   4959   4962 
##      1      1      1      1      1      2      2      1      1      1 
##   4966   4968   4980   4981   4983   4984   4985   4986   4987   4990 
##      1      1      1      1      1      2      1      1      1      1 
##   4994   4996   5000   5001   5003   5005   5006   5007   5010   5014 
##      1      1      3      2      1      2      2      1      1      1 
##   5015   5016   5019   5020   5021   5022   5023   5027   5028   5029 
##      1      3      1      1      1      1      2      3      3      1 
##   5031   5038   5039   5044   5045   5049   5050   5051   5052   5053 
##      1      1      1      1      2      1      1      2      1      1 
##   5055   5061   5062   5065   5068   5075   5078   5081   5084   5088 
##      1      2      1      1      2      1      1      1      2      2 
##   5090   5095   5097   5102   5105   5106   5108   5114   5117   5118 
##      1      2      1      1      1      1      1      2      1      1 
##   5120   5122   5126   5129   5130   5132   5133   5134   5136   5137 
##      3      2      1      1      1      1      1      1      1      1 
##   5138   5140   5147   5148   5149   5150   5152   5153   5156   5157 
##      1      1      2      2      1      1      1      2      1      1 
##   5158   5165   5171   5173   5177   5178   5179   5183   5184   5185 
##      2      1      1      1      1      1      1      1      1      2 
##   5190   5191   5193   5194   5196   5200   5203   5205   5210   5214 
##      2      1      2      1      1      1      1      1      1      2 
##   5221   5223   5229   5240   5245   5246   5247   5248   5253   5254 
##      1      1      1      1      1      1      1      1      1      1 
##   5256   5257   5263   5264   5265   5266   5267   5271   5272   5275 
##      1      1      1      1      1      1      1      1      1      1 
##   5284   5287   5289   5294   5296   5298   5299   5300   5303   5309 
##      1      2      2      1      3      2      1      1      1      1 
##   5315   5318   5321   5322   5323   5326   5328   5333   5336   5342 
##      1      2      1      3      1      2      1      1      2      2 
##   5343   5344   5345   5346   5347   5348   5349   5352   5353   5354 
##      2      1      2      1      1      1      2      1      1      1 
##   5355   5356   5358   5361   5365   5370   5371   5375   5381   5389 
##      1      1      2      3      1      1      2      2      2      1 
##   5391   5394   5396   5397   5402   5405   5407   5409   5414   5416 
##      1      1      1      1      5      1      1      1      1      1 
##   5417   5418   5419   5421   5422   5427   5428   5429   5431   5434 
##      1      1      2      1      1      1      3      1      1      1 
##   5436   5437   5438   5446   5454   5456   5460   5462   5469   5470 
##      1      1      2      1      1      2      1      1      1      1 
##   5473   5474   5477   5482   5487   5488   5491   5492   5494   5495 
##      1      2      1      1      3      1      1      1      1      1 
##   5498   5499   5503   5504   5505   5512   5513   5514   5515   5516 
##      1      2      1      1      1      1      1      1      1      1 
##   5517   5520   5521   5522   5528   5531   5533   5534   5536   5537 
##      3      1      1      1      1      1      1      1      1      1 
##   5538   5541   5542   5546   5549   5552   5554   5560   5561   5562 
##      1      1      1      2      2      1      1      1      1      1 
##   5564   5570   5571   5572   5574   5575   5577   5581   5582   5583 
##      1      1      2      1      1      3      1      1      1      3 
##   5590   5595   5600   5601   5602   5604   5605   5607   5608   5614 
##      2      2      2      1      1      1      1      1      1      1 
##   5616   5627   5629   5633   5635   5639   5647   5650   5653   5654 
##      1      2      1      1      1      1      1      1      1      1 
##   5655   5661   5662   5665   5669   5678   5685   5687   5688   5690 
##      2      1      1      1      1      1      2      1      2      2 
##   5691   5695   5697   5703   5704   5708   5710   5711   5714   5715 
##      1      1      1      2      2      1      1      1      1      1 
##   5717   5718   5720   5722   5723   5724   5727   5730   5731   5732 
##      1      1      1      1      1      2      2      3      1      1 
##   5736   5740   5746   5754   5760   5763   5765   5776   5779   5782 
##      1      1      1      2      1      2      1      1      1      1 
##   5783   5785   5788   5795   5796   5797   5800   5804   5805   5811 
##      1      2      1      1      1      1      1      1      1      1 
##   5819   5822   5823   5830   5834   5835   5836   5838   5842   5844 
##      1      1      1      1      1      1      1      1      1      1 
##   5845   5846   5848   5849   5853   5854   5857   5859   5866   5867 
##      2      1      2      1      2      1      1      1      1      1 
##   5868   5874   5875   5877   5879   5881   5882   5886   5894   5895 
##      1      1      1      1      1      1      1      1      1      1 
##   5902   5904   5907   5908   5913   5917   5919   5922   5924   5927 
##      1      3      1      1      1      1      1      1      1      1 
##   5930   5935   5936   5938   5944   5947   5948   5956   5958   5961 
##      1      1      1      1      1      1      1      1      1      2 
##   5962   5963   5976   5979   5980   5981   5982   5984   5986   5990 
##      1      2      2      1      1      1      1      1      2      1 
##   5992   5996   5997   5998   6003   6004   6009   6011   6015   6016 
##      2      1      1      1      2      1      2      2      2      1 
##   6026   6029   6031   6034   6039   6042   6043   6046   6055   6056 
##      1      3      1      1      1      1      1      1      2      1 
##   6057   6059   6062   6063   6068   6069   6082   6085   6087   6089 
##      1      1      1      1      1      1      1      1      1      1 
##   6090   6092   6097   6105   6109   6114   6123   6127   6128   6129 
##      1      1      3      1      1      1      2      1      1      1 
##   6132   6136   6138   6143   6149   6151   6154   6156   6166   6170 
##      1      1      1      1      2      1      1      2      1      2 
##   6172   6174   6175   6177   6179   6188   6189   6195   6198   6200 
##      1      1      1      1      1      2      2      1      1      1 
##   6202   6203   6204   6206   6211   6214   6215   6222   6223   6226 
##      1      1      3      1      1      1      1      1      2      1 
##   6230   6234   6235   6237   6238   6239   6253   6256   6265   6266 
##      1      1      4      1      1      1      1      1      1      1 
##   6267   6271   6272   6274   6277   6280   6288   6295   6296   6297 
##      1      1      1      1      1      1      1      1      1      1 
##   6299   6304   6307   6309   6312   6314   6317   6321   6325   6333 
##      1      1      1      1      1      1      1      1      1      1 
##   6336   6338   6339   6340   6343   6344   6345   6353   6355   6357 
##      1      1      1      1      1      1      1      1      2      1 
##   6360   6371   6372   6377   6384   6386   6387   6388   6389   6391 
##      1      1      2      2      1      2      2      1      1      1 
##   6393   6397   6398   6403   6404   6407   6413   6418   6423   6424 
##      1      1      1      1      1      1      1      1      1      2 
##   6426   6431   6437   6438   6439   6440   6442   6450   6451   6453 
##      2      1      1      1      1      3      1      1      1      1 
##   6458   6460   6461   6465   6466   6476   6478   6482   6485   6490 
##      1      4      1      1      1      2      1      1      1      1 
##   6493   6497   6498   6500   6501   6507   6511   6515   6516   6520 
##      1      1      1      1      1      1      1      2      2      1 
##   6530   6534   6536   6540   6547   6551   6554   6557   6558   6560 
##      1      1      1      2      1      3      1      1      1      2 
##   6569   6581   6582   6584   6585   6586   6589   6592   6594   6611 
##      1      2      1      1      1      2      1      1      1      1 
##   6614   6615   6619   6621   6625   6632   6644   6645   6646   6648 
##      1      1      2      1      1      2      1      1      1      1 
##   6652   6653   6654   6658   6660   6661   6664   6676   6683   6691 
##      1      1      1      2      2      1      1      1      1      1 
##   6692   6699   6700   6703   6704   6707   6715   6717   6725   6728 
##      1      1      1      1      1      1      1      2      1      1 
##   6730   6731   6733   6734   6736   6742   6746   6748   6749   6750 
##      1      1      1      1      1      1      2      1      1      1 
##   6751   6753   6755   6762   6763   6767   6768   6770   6775   6777 
##      1      1      1      2      1      1      2      1      1      1 
##   6779   6782   6784   6786   6787   6788   6791   6792   6796   6799 
##      3      1      1      1      1      1      1      1      2      1 
##   6801   6802   6809   6819   6820   6822   6823   6842   6846   6851 
##      2      1      2      2      1      1      1      1      1      1 
##   6857   6863   6870   6875   6876   6878   6887   6891   6895   6896 
##      1      2      1      3      1      1      1      1      1      1 
##   6897   6909   6925   6926   6928   6931   6933   6934   6937   6940 
##      1      2      1      1      1      1      1      2      1      1 
##   6942   6943   6944   6949   6952   6954   6957   6959   6960   6973 
##      2      1      1      2      1      1      1      1      1      1 
##   6978   6980   6983   7000   7006   7009   7010   7011   7012   7017 
##      1      1      1      1      1      1      1      1      1      1 
##   7018   7019   7025   7026   7030   7034   7035   7041   7042   7044 
##      1      1      1      1      1      1      2      1      1      1 
##   7045   7053   7054   7061   7063   7065   7075   7078   7080   7081 
##      1      1      1      1      1      1      2      2      1      1 
##   7092   7093   7096   7097   7098   7101   7105   7112   7121   7122 
##      1      3      2      2      1      1      1      1      1      1 
##   7126   7132   7134   7137   7141   7144   7149   7150   7163   7165 
##      3      1      1      2      2      1      1      1      1      1 
##   7173   7181   7184   7189   7196   7205   7207   7213   7215   7223 
##      1      1      1      1      1      1      1      3      1      1 
##   7227   7229   7235   7240   7250   7262   7266   7268   7273   7274 
##      1      1      1      1      2      2      1      1      1      2 
##   7275   7280   7282   7287   7294   7300   7301   7302   7305   7306 
##      1      1      1      1      1      1      1      1      1      2 
##   7307   7308   7311   7312   7313   7316   7321   7323   7324   7325 
##      1      1      1      2      1      1      1      1      1      3 
##   7330   7337   7338   7342   7344   7347   7348   7356   7359   7365 
##      1      1      2      1      1      1      1      1      1      2 
##   7374   7376   7377   7378   7384   7393   7395   7396   7399   7400 
##      1      1      1      2      1      1      1      1      1      2 
##   7403   7404   7405   7413   7415   7419   7420   7422   7431   7433 
##      1      1      1      1      1      1      3      1      1      1 
##   7438   7439   7447   7452   7455   7456   7457   7458   7461   7463 
##      2      2      1      1      2      1      1      1      1      2 
##   7471   7474   7475   7481   7482   7484   7486   7488   7494   7496 
##      1      2      1      1      1      2      2      1      1      1 
##   7499   7501   7507   7510   7514   7522   7523   7524   7531   7538 
##      1      3      1      1      1      1      2      1      1      2 
##   7540   7543   7550   7551   7556   7561   7563   7566   7573   7579 
##      1      2      4      1      1      1      1      1      1      1 
##   7583   7595   7597   7598   7604   7605   7608   7626   7627   7642 
##      1      1      1      1      1      2      1      1      2      1 
##   7643   7644   7657   7659   7661   7662   7671   7672   7682   7684 
##      1      1      1      3      1      2      1      1      1      1 
##   7693   7694   7698   7702   7704   7712   7719   7720   7730   7733 
##      1      1      2      1      3      1      1      1      1      2 
##   7742   7744   7748   7750   7752   7756   7762   7766   7768   7769 
##      1      1      1      3      2      1      1      1      1      1 
##   7773   7775   7779   7786   7787   7798   7800   7806   7807   7811 
##      1      1      2      1      1      1      1      1      1      1 
##   7816   7817   7822   7823   7825   7846   7852   7856   7857   7862 
##      1      1      1      1      1      1      2      2      2      2 
##   7865   7867   7873   7879   7886   7887   7888   7890   7896   7898 
##      1      1      2      1      1      1      1      1      1      1 
##   7900   7901   7903   7906   7907   7911   7923   7926   7927   7933 
##      1      1      1      1      1      1      1      1      1      1 
##   7934   7936   7939   7940   7949   7950   7951   7952   7953   7956 
##      1      1      1      1      1      1      2      1      1      1 
##   7957   7962   7964   7967   7971   7972   7979   7983   7984   7985 
##      1      1      1      1      3      1      2      1      1      1 
##   7997   8000   8008   8010   8017   8020   8023   8024   8028   8029 
##      1      1      1      1      1      1      1      1      1      1 
##   8034   8036   8037   8038   8040   8044   8047   8051   8054   8061 
##      2      1      1      1      2      1      1      2      1      1 
##   8063   8066   8079   8083   8084   8091   8095   8102   8109   8110 
##      1      1      1      1      1      1      1      1      1      1 
##   8114   8120   8122   8128   8129   8134   8136   8137   8142   8146 
##      1      1      3      1      1      1      1      1      1      2 
##   8147   8148   8150   8162   8163   8166   8168   8169   8170   8173 
##      1      1      1      2      1      2      1      1      1      1 
##   8174   8176   8177   8181   8186   8211   8217   8219   8226   8237 
##      1      1      1      2      1      1      1      1      1      1 
##   8238   8243   8246   8252   8257   8262   8265   8272   8274   8278 
##      1      1      1      1      1      1      1      1      2      1 
##   8279   8282   8283   8287   8289   8292   8297   8301   8304   8313 
##      2      2      2      1      1      1      1      1      2      3 
##   8314   8325   8333   8334   8343   8344   8349   8352   8355   8358 
##      1      1      1      1      1      1      1      1      1      1 
##   8359   8364   8369   8384   8385   8388   8400   8411   8415   8422 
##      3      1      1      1      1      1      2      1      1      1 
##   8427   8428   8451   8452   8453   8461   8462   8463   8465   8466 
##      1      1      1      1      1      2      1      2      1      2 
##   8482   8487   8488   8492   8493   8495   8496   8513   8515   8536 
##      2      1      1      1      1      1      1      2      1      1 
##   8545   8546   8549   8552   8572   8576   8579   8586   8588   8589 
##      1      1      1      1      1      2      1      1      1      1 
##   8592   8593   8598   8601   8602   8603   8609   8619   8627   8637 
##      1      1      1      1      1      1      1      3      1      1 
##   8640   8645   8659   8660   8664   8665   8678   8679   8706   8716 
##      1      1      1      1      1      1      1      1      1      1 
##   8718   8721   8728   8731   8741   8743   8745   8746   8752   8753 
##      1      1      1      1      1      1      1      2      1      1 
##   8755   8761   8767   8768   8773   8776   8780   8782   8789   8793 
##      1      1      1      1      2      1      1      1      2      1 
##   8798   8799   8804   8813   8816   8820   8825   8828   8829   8844 
##      1      1      2      1      2      1      1      1      1      2 
##   8873   8877   8882   8886   8889   8897   8900   8908   8910   8912 
##      3      1      1      1      1      1      1      1      1      1 
##   8918   8921   8922   8923   8925   8926   8928   8929   8931   8935 
##      1      1      1      1      1      1      1      1      1      1 
##   8938   8947   8948   8950   8952   8957   8958   8959   8961   8978 
##      1      1      2      1      1      1      1      1      2      1 
##   8980   8983   8988   8997   9000   9008   9009   9012   9015   9018 
##      2      1      1      1      1      1      1      1      1      1 
##   9023   9039   9040   9043   9046   9047   9050   9055   9059   9063 
##      3      1      1      1      1      1      1      1      1      1 
##   9069   9081   9086   9087   9091   9093   9105   9110   9113   9116 
##      1      1      1      1      2      1      1      1      2      1 
##   9117   9122   9129   9136   9138   9152   9153   9156   9160   9163 
##      1      1      2      1      1      1      2      1      1      1 
##   9168   9172   9173   9180   9183   9185   9188   9195   9198   9201 
##      1      1      1      1      1      3      1      1      1      1 
##   9205   9213   9218   9219   9243   9254   9258   9267   9273   9285 
##      1      1      1      1      1      1      2      1      1      1 
##   9300   9319   9320   9321   9324   9342   9343   9348   9350   9353 
##      1      1      1      3      1      1      1      1      1      2 
##   9375   9379   9380   9384   9388   9401   9406   9422   9425   9431 
##      2      1      2      1      1      1      1      1      2      1 
##   9437   9440   9448   9453   9454   9457   9462   9466   9467   9482 
##      1      1      1      1      1      2      1      2      1      1 
##   9484   9493   9497   9510   9511   9516   9537   9545   9548   9549 
##      1      1      2      1      1      1      1      1      1      1 
##   9562   9567   9574   9580   9581   9585   9609   9614   9620   9637 
##      1      1      1      1      1      1      1      1      1      1 
##   9639   9642   9650   9657   9660   9662   9665   9666   9669   9670 
##      1      1      1      1      1      1      1      1      1      1 
##   9673   9674   9682   9687   9698   9699   9700   9702   9714   9715 
##      1      1      1      2      1      1      1      1      1      1 
##   9716   9728   9731   9737   9743   9746   9749   9750   9753   9755 
##      1      1      1      1      1      1      1      1      1      2 
##   9763   9771   9776   9778   9782   9785   9790   9795   9802   9807 
##      1      4      1      2      1      1      1      2      1      1 
##   9813   9814   9816   9825   9838   9848   9857   9860   9867   9868 
##      1      1      1      1      1      1      1      1      1      2 
##   9869   9879   9912   9927   9935   9937   9938   9941   9943   9951 
##      1      1      1      1      1      1      1      1      2      1 
##   9956   9959   9963   9964   9970   9974   9977   9979   9984   9987 
##      1      1      1      1      1      1      1      1      2      1 
##   9996   9998   9999  10006  10013  10026  10028  10037  10047  10054 
##      1      1      2      1      1      1      2      1      1      1 
##  10056  10068  10076  10078  10083  10084  10085  10096  10100  10108 
##      3      1      3      1      1      2      1      1      1      1 
##  10115  10134  10137  10146  10147  10149  10151  10153  10159  10167 
##      1      2      2      1      2      1      1      1      1      1 
##  10169  10176  10177  10178  10188  10193  10197  10198  10207  10221 
##      1      1      1      2      1      1      2      1      1      1 
##  10224  10232  10235  10238  10239  10240  10251  10253  10262  10274 
##      1      1      2      1      2      1      3      1      1      1 
##  10278  10280  10281  10284  10285  10293  10298  10299  10302  10304 
##      1      1      1      1      1      2      3      1      1      1 
##  10310  10314  10320  10322  10325  10333  10336  10338  10349  10352 
##      1      1      1      1      1      1      1      2      1      1 
##  10355  10357  10360  10361  10367  10377  10378  10383  10404  10405 
##      1      1      1      1      1      1      1      1      1      1 
##  10414  10418  10428  10433  10438  10445  10450  10455  10458  10467 
##      1      1      1      1      1      1      1      1      1      2 
##  10469  10478  10481  10485  10486  10488  10490  10502  10510  10525 
##      1      1      1      1      2      1      2      2      1      1 
##  10527  10528  10530  10538  10549  10551  10554  10555  10573  10574 
##      1      2      1      1      1      2      1      1      1      1 
##  10577  10584  10585  10597  10599  10602  10603  10605  10611  10612 
##      2      1      1      1      1      3      2      1      1      3 
##  10613  10626  10629  10632  10633  10636  10641  10643  10651  10654 
##      1      2      1      1      1      1      1      1      1      1 
##  10658  10663  10664  10665  10673  10681  10687  10690  10692  10696 
##      2      1      1      1      1      1      1      1      1      2 
##  10700  10705  10711  10716  10719  10720  10721  10727  10730  10747 
##      1      1      1      1      1      1      1      1      1      2 
##  10755  10758  10770  10774  10776  10783  10785  10794  10796  10797 
##      1      1      1      1      1      1      3      1      1      1 
##  10807  10810  10826  10829  10830  10837  10850  10854  10877  10879 
##      1      1      1      1      1      1      1      1      2      1 
##  10884  10892  10913  10926  10930  10937  10942  10944  10948  10961 
##      1      1      1      1      2      1      1      1      1      1 
##  10969  10970  10972  10978  10986  10991  10993  10995  11000  11002 
##      1      2      1      1      1      1      1      3      1      1 
##  11005  11014  11015  11032  11033  11035  11057  11058  11060  11081 
##      1      1      1      1      1      2      1      1      1      1 
##  11091  11092  11105  11108  11113  11126  11130  11133  11134  11135 
##      1      1      1      1      1      1      1      1      1      1 
##  11146  11156  11158  11174  11176  11184  11187  11189  11190  11199 
##      1      1      1      1      1      1      1      1      1      1 
##  11206  11225  11226  11227  11228  11230  11240  11250  11259  11264 
##      1      2      1      1      2      1      1      1      1      1 
##  11277  11278  11280  11287  11297  11300  11303  11316  11319  11320 
##      1      1      1      2      1      1      1      1      1      1 
##  11331  11341  11348  11350  11351  11369  11370  11374  11379  11383 
##      1      1      1      1      1      1      1      1      1      1 
##  11384  11392  11396  11407  11414  11416  11442  11446  11449  11453 
##      1      1      1      1      1      1      1      1      1      1 
##  11459  11480  11501  11502  11510  11512  11518  11520  11524  11527 
##      1      1      1      1      1      1      1      1      1      1 
##  11531  11532  11533  11538  11555  11556  11563  11574  11588  11590 
##      1      1      1      1      1      1      1      1      1      1 
##  11591  11595  11599  11600  11602  11615  11623  11627  11630  11631 
##      1      1      1      1      1      1      1      1      1      2 
##  11640  11645  11652  11661  11671  11678  11679  11682  11699  11700 
##      1      2      1      1      1      1      1      1      2      1 
##  11716  11721  11724  11725  11744  11746  11750  11755  11760  11766 
##      1      1      1      1      3      1      1      1      2      1 
##  11775  11788  11803  11808  11815  11816  11820  11830  11833  11834 
##      1      1      1      1      1      1      1      1      2      1 
##  11839  11858  11867  11882  11896  11898  11907  11914  11918  11926 
##      1      1      1      1      2      1      1      1      1      2 
##  11935  11938  11945  11948  11949  11952  11953  11960  11970  11976 
##      1      2      2      1      1      1      2      1      1      2 
##  11983  11986  11995  12001  12022  12023  12025  12036  12038  12054 
##      1      1      2      1      1      1      1      1      1      1 
##  12055  12058  12071  12077  12080  12082  12101  12104  12112  12113 
##      1      1      1      1      1      2      1      1      1      1 
##  12116  12127  12143  12145  12146  12147  12154  12157  12160  12164 
##      1      1      1      1      1      1      1      1      1      1 
##  12169  12170  12174  12195  12198  12200  12204  12216  12217  12218 
##      1      1      1      1      1      1      1      1      1      1 
##  12225  12226  12233  12237  12238  12241  12252  12262  12277  12278 
##      1      1      1      1      2      1      1      1      1      1 
##  12286  12287  12294  12295  12301  12304  12307  12320  12322  12324 
##      1      1      1      1      1      1      1      1      1      1 
##  12333  12334  12336  12345  12348  12353  12356  12361  12367  12375 
##      1      1      1      1      1      1      1      1      1      2 
##  12379  12382  12384  12386  12395  12403  12404  12417  12420  12426 
##      1      1      1      1      1      1      1      1      2      1 
##  12433  12439  12441  12455  12458  12462  12476  12478  12480  12501 
##      1      1      1      1      1      1      1      1      1      1 
##  12514  12533  12535  12550  12565  12571  12572  12588  12592  12594 
##      1      1      1      1      2      1      1      2      1      2 
##  12607  12608  12622  12638  12639  12642  12656  12668  12676  12684 
##      1      1      1      1      1      1      1      1      1      1 
##  12698  12705  12738  12740  12750  12751  12755  12756  12758  12774 
##      1      2      1      1      1      2      1      1      1      1 
##  12786  12791  12792  12795  12796  12799  12803  12806  12814  12820 
##      1      1      1      1      1      1      1      3      1      1 
##  12833  12834  12843  12849  12850  12851  12864  12881  12890  12898 
##      1      1      1      1      1      1      1      1      1      1 
##  12901  12911  12923  12928  12940  12947  12958  12977  12979  12989 
##      2      2      1      2      1      1      1      1      1      1 
##  12992  12999  13006  13008  13010  13014  13015  13022  13023  13026 
##      1      1      1      1      1      1      1      1      1      1 
##  13031  13036  13052  13053  13063  13067  13070  13072  13078  13084 
##      1      1      1      2      1      1      1      1      1      2 
##  13092  13095  13112  13121  13123  13124  13140  13148  13150  13155 
##      3      1      1      1      2      1      1      1      1      1 
##  13159  13165  13180  13185  13194  13196  13203  13213  13215  13235 
##      4      1      1      1      1      1      1      1      1      1 
##  13236  13239  13248  13252  13256  13258  13259  13271  13279  13280 
##      1      1      2      2      1      2      1      1      1      1 
##  13304  13311  13315  13317  13321  13325  13342  13343  13351  13352 
##      1      1      1      1      1      1      1      2      1      2 
##  13353  13355  13356  13363  13364  13365  13370  13391  13394  13413 
##      1      1      1      1      1      1      1      2      1      1 
##  13414  13432  13433  13452  13460  13466  13471  13487  13495  13498 
##      1      1      1      2      1      1      1      1      2      1 
##  13507  13509  13526  13543  13552  13555  13561  13572  13581  13588 
##      1      1      1      1      1      1      1      1      1      1 
##  13589  13604  13606  13611  13614  13618  13627  13639  13652  13653 
##      1      1      1      1      2      1      2      1      1      1 
##  13655  13672  13675  13680  13695  13721  13723  13727  13728  13733 
##      1      1      1      1      1      1      1      1      1      2 
##  13744  13777  13780  13783  13788  13794  13798  13801  13807  13808 
##      1      1      1      2      2      1      1      1      1      1 
##  13811  13817  13837  13880  13881  13889  13892  13895  13902  13904 
##      1      1      1      1      1      1      1      1      1      1 
##  13931  13934  13937  13939  13953  13967  13970  13972  13986  14010 
##      1      1      1      1      1      1      1      1      1      1 
##  14018  14028  14030  14034  14045  14046  14068  14085  14090  14094 
##      1      1      1      1      2      1      1      1      1      1 
##  14129  14153  14154  14155  14170  14186  14194  14201  14204  14205 
##      1      1      1      1      1      1      1      1      1      1 
##  14210  14211  14212  14222  14223  14228  14238  14239  14251  14256 
##      1      1      1      1      1      1      1      1      1      1 
##  14273  14274  14310  14319  14323  14324  14331  14333  14350  14352 
##      1      1      2      1      1      1      1      1      1      1 
##  14366  14379  14394  14409  14432  14437  14440  14446  14450  14457 
##      1      1      1      1      1      1      1      1      1      1 
##  14464  14485  14489  14500  14503  14504  14505  14515  14517  14519 
##      1      1      1      1      1      1      1      1      1      1 
##  14543  14546  14561  14577  14581  14620  14621  14639  14645  14646 
##      1      1      1      1      1      1      3      4      1      1 
##  14647  14660  14661  14664  14670  14672  14689  14692  14695  14700 
##      1      1      1      1      1      1      1      1      1      1 
##  14712  14729  14731  14738  14747  14750  14755  14760  14767  14771 
##      1      1      1      1      1      1      1      1      1      1 
##  14790  14795  14797  14799  14800  14815  14821  14850  14851  14855 
##      1      1      1      1      1      1      1      1      1      1 
##  14856  14868  14900  14904  14906  14908  14909  14910  14930  14935 
##      1      2      1      1      1      1      1      1      1      1 
##  14939  14941  14977  14981  14982  15019  15021  15023  15024  15027 
##      1      1      1      1      1      1      1      1      1      1 
##  15028  15037  15043  15061  15066  15068  15073  15091  15107  15143 
##      1      1      1      1      1      1      1      1      1      1 
##  15155  15159  15175  15184  15193  15205  15208  15241  15245  15250 
##      1      1      1      1      1      1      1      1      1      1 
##  15251  15270  15281  15302  15312  15330  15335  15336  15340  15356 
##      1      1      1      2      1      1      2      3      1      1 
##  15375  15382  15384  15392  15394  15398  15413  15448  15451  15457 
##      1      1      1      2      2      1      1      1      1      2 
##  15460  15467  15486  15488  15506  15507  15514  15526  15527  15539 
##      1      1      1      1      1      1      1      1      1      1 
##  15543  15547  15549  15564  15565  15567  15568  15571  15591  15598 
##      1      1      1      1      1      1      1      1      1      1 
##  15599  15604  15623  15628  15663  15684  15689  15698  15715  15730 
##      1      1      1      2      1      1      1      1      1      1 
##  15733  15741  15760  15772  15799  15820  15865  15867  15869  15875 
##      1      1      1      1      1      1      1      2      1      1 
##  15882  15883  15890  15896  15899  15906  15914  15920  15942  15954 
##      1      1      1      1      1      1      1      1      1      1 
##  15987  15995  16000  16004  16012  16017  16018  16020  16046  16049 
##      2      1      1      2      1      1      1      1      1      1 
##  16055  16056  16067  16077  16087  16095  16107  16128  16133  16136 
##      1      1      2      1      1      3      1      1      1      1 
##  16142  16159  16167  16181  16191  16201  16226  16255  16257  16302 
##      1      2      1      1      1      1      1      1      2      1 
##  16331  16347  16356  16363  16365  16389  16399  16400  16405  16412 
##      1      1      1      1      1      1      1      2      1      1 
##  16421  16443  16451  16452  16458  16460  16467  16494  16497  16525 
##      1      1      1      1      1      1      1      1      1      1 
##  16546  16547  16563  16567  16574  16584  16586  16592  16594  16610 
##      1      1      1      1      1      1      1      1      1      1 
##  16614  16668  16688  16748  16751  16757  16761  16792  16808  16813 
##      1      2      1      1      1      1      1      1      1      1 
##  16821  16826  16828  16836  16855  16866  16868  16882  16885  16933 
##      1      1      1      1      1      1      1      3      1      1 
##  16942  16953  16970  16975  17000  17002  17009  17012  17032  17042 
##      1      1      1      1      1      1      1      1      1      1 
##  17044  17051  17056  17070  17083  17084  17092  17097  17103  17117 
##      1      1      1      1      1      1      1      1      1      1 
##  17126  17133  17139  17148  17165  17167  17175  17186  17188  17191 
##      1      1      1      1      1      1      1      1      1      1 
##  17197  17201  17203  17209  17219  17234  17252  17261  17273  17290 
##      1      1      1      1      1      1      1      1      1      2 
##  17316  17354  17368  17377  17396  17404  17408  17420  17422  17430 
##      1      1      1      1      2      1      1      1      1      1 
##  17444  17459  17460  17462  17477  17489  17496  17529  17530  17533 
##      1      1      1      1      1      1      1      1      1      1 
##  17546  17547  17560  17588  17590  17591  17594  17597  17607  17643 
##      1      1      1      1      1      1      1      1      1      1 
##  17644  17649  17667  17689  17707  17715  17724  17727  17731  17741 
##      1      1      1      1      1      1      1      1      1      1 
##  17761  17774  17792  17829  17833  17860  17868  17871  17872  17891 
##      2      1      1      1      1      1      1      1      1      1 
##  17895  17909  17911  17920  17943  17984  17989  17998  18037  18067 
##      2      1      1      1      1      1      1      1      1      1 
##  18077  18079  18084  18093  18095  18103  18134  18136  18138  18156 
##      1      1      1      1      1      1      1      1      1      1 
##  18170  18201  18205  18210  18214  18226  18239  18254  18265  18274 
##      1      1      1      1      1      1      1      1      1      1 
##  18288  18302  18312  18319  18324  18325  18330  18340  18344  18352 
##      1      1      1      1      1      1      1      1      2      1 
##  18355  18359  18364  18375  18376  18377  18403  18406  18432  18447 
##      1      1      1      1      1      1      1      1      1      1 
##  18454  18458  18475  18480  18499  18509  18532  18534  18536  18537 
##      1      1      1      1      1      1      1      1      1      1 
##  18547  18576  18580  18581  18584  18628  18632  18652  18667  18671 
##      1      1      1      1      1      3      1      1      1      1 
##  18674  18678  18686  18698  18718  18720  18723  18729  18737  18747 
##      5      2      1      1      1      1      1      1      1      1 
##  18822  18839  18854  18859  18861  18866  18893  18908  18929  18930 
##      1      1      1      1      1      1      1      1      1      2 
##  18932  18971  18978  18983  18986  18992  18998  19014  19018  19038 
##      1      1      2      1      1      1      1      1      1      1 
##  19053  19063  19090  19100  19104  19108  19135  19145  19156  19163 
##      1      1      1      1      1      1      1      1      1      1 
##  19165  19172  19193  19212  19226  19260  19263  19268  19277  19302 
##      1      1      2      1      1      3      1      1      1      2 
##  19315  19321  19328  19341  19349  19369  19401  19403  19435  19453 
##      1      2      1      1      1      1      1      1      1      1 
##  19458  19460  19474  19498  19501  19541  19584  19589  19608  19612 
##      1      1      1      1      1      1      1      1      1      1 
##  19638  19641  19659  19664  19681  19685  19688  19690  19695  19704 
##      1      1      1      2      1      1      1      1      1      1 
##  19707  19710  19722  19725  19726  19738  19754  19756  19772  19773 
##      1      1      2      1      1      1      1      1      1      1 
##  19779  19796  19849  19861  19869  19890  19911  19923  19963  20012 
##      1      1      1      1      1      1      1      1      1      1 
##  20058  20067  20095  20100  20107  20112  20118  20128  20135  20149 
##      1      1      1      1      1      1      1      1      1      1 
##  20150  20164  20172  20185  20207  20210  20218  20235  20241  20285 
##      1      1      1      1      1      1      1      1      1      1 
##  20286  20328  20348  20349  20373  20469  20472  20503  20510  20533 
##      1      1      1      1      1      1      1      1      1      2 
##  20542  20589  20604  20641  20647  20657  20664  20674  20681  20700 
##      1      1      1      1      2      1      1      1      1      1 
##  20729  20730  20763  20779  20785  20811  20851  20869  20874  20886 
##      1      1      1      1      1      1      1      1      1      1 
##  20907  20911  20928  20944  20965  20979  20990  21009  21018  21019 
##      1      1      1      1      1      1      2      1      1      1 
##  21026  21042  21060  21126  21135  21139  21147  21149  21157  21166 
##      1      1      1      1      3      1      1      1      3      1 
##  21195  21216  21251  21266  21276  21285  21297  21299  21323  21350 
##      1      1      1      1      1      1      1      1      1      1 
##  21369  21393  21400  21404  21446  21460  21465  21500  21505  21541 
##      1      2      1      1      1      1      1      1      1      1 
##  21567  21615  21618  21628  21636  21659  21691  21723  21751  21758 
##      1      1      1      1      1      1      1      1      1      1 
##  21783  21844  21858  21891  21893  21904  21905  21909  21928  21944 
##      1      1      1      1      1      1      1      1      1      1 
##  21969  21972  21980  21989  22010  22049  22058  22091  22093  22115 
##      1      1      1      1      1      1      1      1      1      1 
##  22144  22155  22165  22169  22174  22177  22187  22221  22228  22245 
##      1      1      1      1      1      1      1      1      1      1 
##  22264  22271  22273  22284  22291  22307  22332  22397  22431  22435 
##      1      1      1      2      1      1      1      1      1      1 
##  22449  22495  22502  22526  22529  22555  22578  22624  22668  22674 
##      1      1      1      1      1      1      1      1      1      1 
##  22682  22697  22713  22754  22757  22775  22776  22793  22831  22855 
##      1      2      1      1      1      1      1      1      1      2 
##  22871  22882  22889  22903  22922  22925  22929  22947  22963  22969 
##      1      1      1      1      1      1      1      1      1      1 
##  22994  23029  23034  23044  23057  23064  23066  23096  23100  23102 
##      1      1      1      2      1      1      1      4      3      1 
##  23107  23109  23129  23189  23210  23251  23254  23262  23302  23308 
##      1      1      1      1      1      1      1      1      1      1 
##  23320  23368  23415  23423  23472  23473  23476  23505  23511  23535 
##      1      1      1      1      1      1      1      1      2      1 
##  23549  23552  23562  23571  23601  23610  23626  23630  23644  23650 
##      1      1      1      1      1      1      3      1      1      1 
##  23660  23668  23671  23676  23727  23740  23748  23752  23754  23756 
##      2      1      1      1      1      1      1      1      1      2 
##  23759  23772  23802  23835  23867  23880  23931  23960  23973  23983 
##      1      1      1      1      1      1      1      1      1      1 
##  23984  24008  24012  24024  24026  24046  24050  24070  24072  24089 
##      1      1      1      1      1      1      1      1      1      1 
##  24096  24099  24115  24132  24150  24173  24177  24184  24199  24237 
##      1      1      2      1      1      1      1      1      1      1 
##  24251  24270  24280  24291  24297  24350  24351  24364  24400  24413 
##      1      2      1      1      1      1      2      1      1      1 
##  24442  24444  24476  24512  24589  24592  24614  24632  24642  24665 
##      1      1      2      1      1      1      1      1      1      1 
##  24675  24677  24701  24762  24763  24802  24808  24831  24850  24858 
##      1      1      1      1      1      2      1      1      1      1 
##  24865  24871  24910  24940  24975  24981  24998  25000  25018  25045 
##      1      1      1      1      1      1      1      1      1      1 
##  25054  25067  25108  25119  25133  25153  25166  25170  25218  25224 
##      1      1      1      1      1      1      1      1      1      1 
##  25255  25257  25270  25274  25280  25307  25320  25360  25389  25392 
##      1      1      1      1      1      1      1      1      2      1 
##  25464  25476  25500  25512  25579  25589  25611  25623  25627  25645 
##      1      1      1      1      1      1      1      1      1      1 
##  25651  25662  25664  25730  25735  25766  25781  25784  25911  25928 
##      1      1      1      1      1      2      1      1      1      1 
##  25980  26017  26043  26057  26070  26085  26098  26107  26124  26172 
##      1      1      1      1      1      1      1      1      1      1 
##  26175  26231  26331  26403  26412  26436  26450  26487  26536  26593 
##      2      1      1      1      1      1      1      1      1      1 
##  26600  26601  26622  26623  26673  26679  26704  26752  26795  26811 
##      1      1      1      1      2      1      1      1      1      1 
##  26813  26815  26818  26836  26838  26843  26931  26955  26978  26987 
##      1      1      1      1      1      1      1      1      1      1 
##  26989  27011  27021  27031  27060  27065  27075  27090  27098  27106 
##      1      1      1      1      1      1      1      1      1      1 
##  27129  27136  27150  27198  27311  27367  27400  27404  27460  27466 
##      2      1      1      1      1      1      1      1      1      2 
##  27491  27528  27551  27558  27649  27651  27663  27719  27755  27784 
##      1      1      1      1      1      1      1      1      1      1 
##  27787  27870  27883  27898  27927  27969  27997  28014  28034  28057 
##      1      1      1      1      1      1      1      1      1      1 
##  28065  28070  28094  28114  28125  28133  28147  28172  28174  28175 
##      1      1      1      1      1      1      1      1      1      1 
##  28200  28247  28255  28260  28277  28389  28410  28433  28463  28464 
##      1      2      1      1      1      1      1      1      1      1 
##  28473  28502  28504  28505  28587  28591  28600  28649  28667  28681 
##      1      1      1      1      1      2      1      1      1      1 
##  28684  28740  28782  28840  28929  28963  29072  29074  29082  29119 
##      1      1      1      1      1      1      2      1      1      1 
##  29140  29156  29183  29207  29246  29285  29319  29335  29369  29375 
##      1      1      1      1      1      1      1      1      1      1 
##  29403  29429  29446  29448  29487  29489  29537  29687  29688  29719 
##      1      1      1      1      1      1      1      1      1      1 
##  29776  29795  29809  29875  29876  29882  29997  30023  30027  30097 
##      1      2      1      1      1      1      1      1      1      1 
##  30112  30119  30202  30231  30239  30347  30402  30408  30417  30441 
##      1      1      1      1      1      1      1      1      1      1 
##  30453  30500  30520  30563  30579  30588  30645  30664  30667  30682 
##      1      1      1      1      1      1      1      1      1      1 
##  30691  30747  30777  30803  30920  30928  30948  30970  30997  30998 
##      1      1      1      1      1      1      1      1      1      1 
##  31013  31031  31035  31041  31099  31115  31176  31251  31297  31348 
##      1      1      1      1      1      1      1      1      1      1 
##  31352  31392  31404  31497  31533  31541  31550  31605  31622  31631 
##      1      1      1      1      1      1      1      1      1      1 
##  31761  31847  31894  31913  31919  32005  32006  32069  32110  32119 
##      1      1      1      1      1      1      1      1      1      1 
##  32138  32175  32200  32254  32326  32390  32396  32413  32497  32500 
##      1      1      1      1      1      1      1      1      1      1 
##  32576  32645  32683  32698  32755  32766  32790  32859  32946  32961 
##      1      1      1      1      1      1      1      1      1      1 
##  32969  33036  33057  33134  33135  33154  33240  33323  33324  33337 
##      3      1      1      1      1      2      1      1      1      1 
##  33376  33432  33463  33506  33509  33520  33555  33566  33628  33646 
##      1      1      1      1      1      1      1      1      1      1 
##  33773  33783  33801  33803  33835  33852  33863  33888  33925  33929 
##      1      1      1      1      1      1      1      1      1      1 
##  33998  34133  34171  34183  34193  34225  34336  34381  34388  34416 
##      1      1      1      1      1      1      1      1      1      1 
##  34434  34435  34525  34555  34645  34666  34794  34836  34874  34876 
##      1      1      1      1      1      1      1      1      2      1 
##  34880  34899  34911  34968  34977  34988  34990  34997  35008  35055 
##      1      2      1      1      1      1      1      1      1      1 
##  35096  35097  35119  35128  35169  35185  35212  35227  35250  35299 
##      1      1      1      1      1      1      1      1      1      1 
##  35334  35374  35454  35457  35459  35471  35514  35574  35727  35794 
##      1      1      1      1      1      1      1      1      3      1 
##  35849  35901  35927  35972  36153  36302  36363  36384  36471  36477 
##      2      1      1      1      1      1      1      1      1      1 
##  36492  36514  36598  36626  36863  36961  37003  37077  37212  37287 
##      1      1      1      1      1      1      1      1      1      1 
##  37291  37316  37317  37329  37339  37454  37463  37534  37642  37643 
##      1      1      1      1      1      2      1      1      1      1 
##  37655  37837  37855  37919  37936  37998  38068  38108  38149  38160 
##      1      1      1      1      1      1      1      1      1      1 
##  38212  38286  38304  38336  38365  38417  38432  38475  38489  38657 
##      1      1      1      1      1      1      1      1      1      1 
##  38660  38664  38665  38709  38870  38960  38996  39011  39028  39210 
##      3      1      1      1      1      1      1      1      1      1 
##  39227  39295  39379  39409  39470  39473  39484  39632  39856  39986 
##      1      1      1      1      1      1      1      1      1      1 
##  40013  40087  40189  40335  40389  40392  40482  40485  40527  40553 
##      1      2      1      1      1      1      1      1      1      1 
##  40633  40779  40836  40938  41014  41020  41214  41244  41361  41374 
##      1      2      1      1      1      4      1      1      1      1 
##  41378  41386  41661  41694  41763  41822  41975  42205  42342  42370 
##      1      1      1      1      1      1      1      1      1      1 
##  42387  42485  42488  42556  42824  42854  42881  42962  43064  43079 
##      1      1      1      1      1      1      1      1      1      1 
##  43093  43121  43200  43322  43363  43367  43437  43607  43642  43722 
##      1      1      1      1      1      1      1      1      1      1 
##  43761  43776  43789  43958  44036  44203  44262  44307  44369  44493 
##      1      1      1      1      1      1      1      1      1      1 
##  44734  44744  44859  44879  45059  45201  45202  45298  45364  45655 
##      1      1      1      1      1      1      1      1      1      1 
##  45726  45857  45864  45979  46010  46065  46099  46127  46216  46255 
##      1      1      1      1      1      1      1      1      2      1 
##  46331  46359  46394  46642  46943  46989  47008  47371  47625  47746 
##      1      1      1      1      1      1      1      1      1      1 
##  47766  47918  47963  47965  48009  48024  48100  48121  48150  48201 
##      1      1      1      1      1      1      1      1      2      1 
##  48289  48423  48487  48673  48703  48865  48992  49047  49116  49178 
##      1      1      1      2      1      1      1      1      1      1 
##  49229  49248  49274  49283  49454  49466  49759  49809  49818  49868 
##      1      1      1      1      1      1      1      1      1      1 
##  49924  50017  50163  50261  50385  50396  50421  50610  50688  50852 
##      1      1      1      1      1      1      1      1      1      1 
##  51103  51119  51252  51344  51370  51788  51847  52033  52047  52379 
##      1      1      1      1      1      1      1      1      1      1 
##  52456  52480  52612  52820  52844  53054  53083  53148  53215  53335 
##      1      1      1      1      1      1      1      1      1      1 
##  53351  53420  53439  53442  53622  53798  53824  54000  54007  54068 
##      1      1      1      1      1      1      1      1      1      1 
##  54364  54480  54550  54596  54782  54881  54915  54918  55111  55462 
##      1      1      1      1      1      1      1      1      1      1 
##  55716  55869  55958  56254  56288  56502  56716  56743  57252  57265 
##      1      1      1      1      1      1      1      1      1      1 
##  57376  57580  57884  57979  58221  58365  58463  58521  58565  58583 
##      1      1      1      1      1      1      1      1      1      1 
##  58678  58708  58858  59241  59415  59613  59692  59860  59883  60170 
##      1      1      1      1      1      1      2      1      1      1 
##  60308  60310  60346  60433  60510  60571  60616  60966  60997  61085 
##      1      1      1      1      1      1      1      1      1      1 
##  61231  61350  61393  61442  61564  61635  61745  61821  61981  62092 
##      1      1      1      1      1      1      1      1      1      1 
##  62129  62259  62312  62348  62512  62891  62903  63047  63217  63290 
##      1      1      1      1      1      1      1      1      1      1 
##  63373  63482  63558  63743  63897  64116  64420  64519  64538  64587 
##      1      1      1      2      1      1      1      1      1      1 
##  64595  64839  64868  65216  65320  65938  65951  65959  66422  66466 
##      1      1      1      1      1      1      1      1      1      1 
##  66600  66852  67434  67449  68013  68123  68304  68587  68828  68900 
##      1      1      1      1      1      2      1      1      1      1 
##  69276  69313  69483  69551  69823  69875  69907  70000  70132  70146 
##      1      1      1      1      1      1      1      1      1      1 
##  70334  70456  70567  70659  70734  70983  71328  72051  72112  72113 
##      1      1      1      5      1      1      1      1      1      1 
##  72121  72156  72302  72313  72705  72817  72997  73118  73323  73490 
##      1      1      1      1      1      1      1      1      1      1 
##  73661  73936  74579  74844  74990  75492  76008  76588  76840  77300 
##      1      2      2      1      1      1      1      1      1      1 
##  77384  77422  77771  77853  77985  78097  78380  78750  78935  79522 
##      1      1      1      1      1      1      1      1      1      1 
##  79574  80097  80346  80441  80646  80792  80975  81004  81495  81723 
##      1      1      1      1      1      1      1      1      1      1 
##  82271  82580  82708  82980  83138  83534  83756  83956  84427  84691 
##      1      1      1      1      1      1      1      1      1      1 
##  84834  84933  85065  85803  85885  85953  86101  86127  86282  86303 
##      1      1      1      1      1      1      1      1      1      1 
##  86351  86566  86730  87588  89000  89265  89523  89827  90536  90588 
##      2      1      1      1      1      1      1      1      1      1 
##  90756  91162  91501  91554  91636  91687  92177  92467  92753  93237 
##      1      1      1      1      1      1      2      1      1      1 
##  93593  95043  95280  95320  95389  95441  97020  97773  99792  99979 
##      1      1      1      1      1      1      1      1      1      1 
##  99991 101212 101497 101512 101644 102546 102936 102959 103076 103505 
##      2      1      1      1      1      1      1      2      1      1 
## 103709 103884 103975 104768 105340 105575 106071 106156 107319 107354 
##      1      1      1      1      1      1      2      1      1      1 
## 108415 109820 109956 110541 111524 111690 111873 112221 112684 113205 
##      1      1      1      1      1      1      1      1      1      1 
## 113552 114385 114872 116014 116896 117937 119147 119660 120153 120642 
##      1      1      1      1      1      1      1      1      1      1 
## 121379 122690 122868 123828 123871 124318 124471 124651 124691 124858 
##      1      1      1      1      1      1      1      2      1      1 
## 124888 126638 126830 127058 127472 127850 128639 128864 128993 129746 
##      1      1      1      1      1      1      2      1      1      1 
## 130093 131214 134322 135229 136476 142263 143329 144886 145618 149901 
##      1      1      1      3      1      1      1      1      2      1 
## 153237 155578 157422 158486 160039 161344 161475 161782 164607 165097 
##      1      1      1      1      1      1      1      1      1      1 
## 168648 171093 172240 173334 174862 175281 176347 179158 183396 188818 
##      1      1      1      1      1      1      1      1      1      1 
## 190585 192016 202741 205400 215315 223738 225595 230291 241707 242333 
##      1      1      1      1      1      1      1      1      1      1 
## 249209 255963 265084 279970 284169 327677 444745 463881 
##      1      1      1      1      1      1      1      1
ggplot(data = DelinquenciesValues, aes(x = AmountDelinquent))+
  geom_histogram()+
  ggtitle('Count of Amount Delinquent')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

summary(loans$AmountDelinquent)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
##      0.0      0.0      0.0    984.5      0.0 463881.0     7622
head(sort(table(loans$AmountDelinquent), decreasing = TRUE), 50)
## 
##     0    50   100    25    30    75    60    40   120    15    55    65 
## 89818    73    67    66    65    56    46    43    35    34    34    34 
##    67   150   130    10    20    35    70   200    80    33    45    54 
##    32    32    31    30    30    29    29    29    28    27    26    26 
##    79   110   300    36    51    57    68    88    90   105   134    32 
##    26    26    26    25    25    25    25    25    25    25    25    24 
##    48    52    84   230    53    78   101   115   158   350    31    37 
##    24    24    24    24    23    23    23    23    23    23    22    22 
##    42    64 
##    22    22
DelinquenciesValues <- subset(loans, loans$AmountDelinquent != 0)
table(DelinquenciesValues$AmountDelinquent)
## 
##      1      2      3      4      5      6      7      8      9     10 
##      7     10      7      6      9      9      5      6      7     30 
##     11     12     13     14     15     16     17     18     19     20 
##      8      9     12     12     34      6     12      6      8     30 
##     21     22     23     24     25     26     27     28     29     30 
##      8     11      8     12     66     14     15     19     15     65 
##     31     32     33     34     35     36     37     38     39     40 
##     22     24     27     20     29     25     22     12     14     43 
##     41     42     43     44     45     46     47     48     49     50 
##     15     22     21     18     26     19     21     24     15     73 
##     51     52     53     54     55     56     57     58     59     60 
##     25     24     23     26     34     21     25     17     17     46 
##     61     62     63     64     65     66     67     68     69     70 
##     17     18     18     22     34     22     32     25     13     29 
##     71     72     73     74     75     76     77     78     79     80 
##     22     17     11     20     56     21     17     23     26     28 
##     81     82     83     84     85     86     87     88     89     90 
##     19     19     15     24     18     19     18     25     13     25 
##     91     92     93     94     95     96     97     98     99    100 
##     13     15     22     22     16     12     20     21     13     67 
##    101    102    103    104    105    106    107    108    109    110 
##     23     19     21     16     25     19     21     17     13     26 
##    111    112    113    114    115    116    117    118    119    120 
##     14     21     19     19     23     20     17     16     15     35 
##    121    122    123    124    125    126    127    128    129    130 
##     13     12     16     13     18     13     11     11     22     31 
##    131    132    133    134    135    136    137    138    139    140 
##     15     20     14     25     21      7      9     19      9     19 
##    141    142    143    144    145    146    147    148    149    150 
##     11     13     14     10     18     12     16     11     13     32 
##    151    152    153    154    155    156    157    158    159    160 
##     14     15     21     11      9     13     11     23      7     15 
##    161    162    163    164    165    166    167    168    169    170 
##     15     14      9     13     10     17     18     12      9     10 
##    171    172    173    174    175    176    177    178    179    180 
##     13     14      9     18     17     11      7     20     14     15 
##    181    182    183    184    185    186    187    188    189    190 
##     12     12     14      9     21      9      8     10     13      9 
##    191    192    193    194    195    196    197    198    199    200 
##     16     13      9     10     10      8     11      9      9     29 
##    201    202    203    204    205    206    207    208    209    210 
##     11     16     12      7      7     15     13      7     14     14 
##    211    212    213    214    215    216    217    218    219    220 
##     10      8     12     18      7      9      9      9      9     18 
##    221    222    223    224    225    226    227    228    229    230 
##      9      6     20     13     15      8     13     20     12     24 
##    231    232    233    234    235    236    237    238    239    240 
##     13      9      9     13      9      9      5      9     10      8 
##    241    242    243    244    245    246    247    248    249    250 
##      9      6      9      8     13     13     10     15     10     20 
##    251    252    253    254    255    256    257    258    259    260 
##     10     11     13     13     12      9     13     15     14     12 
##    261    262    263    264    265    266    267    268    269    270 
##      7      9      9      9     10     13     14      7     19      9 
##    271    272    273    274    275    276    277    278    279    280 
##      7      5     10     10      7     11      7     10     18     15 
##    281    282    283    284    285    286    287    288    289    290 
##     12      4     12     12     14     11      6      9      8     12 
##    291    292    293    294    295    296    297    298    299    300 
##      9      9      8     12     14     14     10     11     10     26 
##    301    302    303    304    305    306    307    308    309    310 
##     10      8      5      8      5     11     10     12      6      8 
##    311    312    313    314    315    316    317    318    319    320 
##      8      4     11      8     10     13      4     10      9     11 
##    321    322    323    324    325    326    327    328    329    330 
##      4      7      4      7      9      5      9      3      3     11 
##    331    332    333    334    335    336    337    338    339    340 
##      6      8      2      4      4     10     10      8      4      8 
##    341    342    343    344    345    346    347    348    349    350 
##      7      7      7      8      2      6      3     10     10     23 
##    351    352    353    354    355    356    357    358    359    360 
##      7     12     12      3      9      8     10     11      6     10 
##    361    362    363    364    365    366    367    368    369    370 
##      6      4     11      5      7      8     10     14      8     15 
##    371    372    373    374    375    376    377    378    379    380 
##      5      9      2      5      8      5      7      9     10     10 
##    381    382    383    384    385    386    387    388    389    390 
##      9     11      9      3      7      8      7      7      6      9 
##    391    392    393    394    395    396    397    398    399    400 
##      6      6      9      4      6      6      5      8      3     16 
##    401    402    403    404    405    406    407    408    409    410 
##     11      8     15      4      7      2      4      7      8      6 
##    411    412    413    414    415    416    417    418    419    420 
##      7      7      6      5      4      9      8      5      6      7 
##    421    422    423    424    425    426    427    428    429    430 
##      4      6      7      6      8      9      6      9      7      5 
##    431    432    433    434    435    436    437    438    439    440 
##      8      4     16      3      3      7      4     10      5      7 
##    441    442    443    444    445    446    447    448    449    450 
##      5      2      4      5      2      9     10      8      4     12 
##    451    452    453    454    455    456    457    458    459    460 
##      5      3      2      7      4      4     10      6      6     15 
##    461    463    464    465    466    467    468    469    470    471 
##      6      8      2      5      4      4      7      5      4      3 
##    472    473    474    475    476    477    478    479    480    481 
##      7      2      7     10      9      5      8      8      6      3 
##    482    483    484    485    486    487    488    489    490    491 
##     10      5      4      5      9      2      4      4     10      6 
##    492    493    494    495    496    497    498    499    500    501 
##      3      3      9     13      6      8      5      6     11      4 
##    502    503    504    505    506    507    508    509    510    511 
##      7      4      6      5      8      2      7      2      8      5 
##    512    513    514    515    516    517    518    519    520    521 
##      7      4      8      7      1      2      9      4      7      5 
##    522    523    524    525    526    527    528    529    530    531 
##      5      3      1     11      8      5      4      5      5      4 
##    532    533    534    535    536    537    538    539    540    541 
##      6      6     10      8     10      2      5      5      5      6 
##    542    543    544    545    546    547    548    549    550    551 
##      5      8      2      5      6      6      7      6      7      4 
##    552    553    554    555    556    557    558    559    560    561 
##      7      7      3      4      3      4      2      4      8      7 
##    562    563    564    565    566    567    568    569    570    571 
##      2      3      2      3      7      7      6      6      8      5 
##    572    573    574    575    576    577    578    579    580    581 
##      6      3      3      3      4      8      4      6      3      2 
##    582    583    584    585    586    587    588    589    590    591 
##      4      5      6      3      4      8      2      6     11      8 
##    592    593    594    595    596    597    598    599    600    601 
##      3      2      1      7      8      7      5      4     17      3 
##    602    603    604    605    606    607    608    609    610    611 
##      3      8      2      4      2      3      5      8      6      7 
##    612    613    614    615    616    617    618    619    620    621 
##      2      6      5      4      4      4      7     10      7      2 
##    622    623    624    625    626    627    628    630    631    632 
##      3      5      6      2      4      4      3     10      3      5 
##    633    634    635    636    637    638    639    640    641    642 
##      9      2      5      2      7      5      3      5      7      5 
##    643    644    645    646    647    648    649    650    651    652 
##      4     10      4      3      5      9      2     12      2      3 
##    653    654    655    656    657    658    659    660    661    662 
##      3      6      4      8      6      5      5      7      5      6 
##    663    664    665    666    667    668    669    670    671    672 
##      3      7      2     11      4      4      3      2     11      5 
##    673    674    675    676    677    678    679    680    681    682 
##      4      3      5      3      7      5      3      3      2      2 
##    683    684    686    687    688    689    690    691    692    693 
##      5      2     10      2      3      6      3      6      8      5 
##    694    695    696    697    698    699    700    701    702    703 
##      9      4      2      1      6      1     10      2      2      5 
##    704    705    706    707    708    709    710    711    712    713 
##      3      1      7      6      5      2      6      5      4      5 
##    714    715    716    717    718    719    720    721    722    723 
##      2      6      3      1      2      4      4      4      4      5 
##    724    725    726    727    728    729    730    731    732    733 
##      3      7      9      3      4      2      2      4      2      3 
##    734    735    736    737    738    739    740    741    742    743 
##      1      4      6      4      1      5      5      1      2      2 
##    744    745    746    747    748    749    750    751    752    753 
##      3      1      2      1      5      1     10      8      6      5 
##    754    755    756    757    758    759    760    761    762    763 
##      5      7      2      4      6      2      3      4      4      2 
##    764    765    766    767    768    769    770    771    772    773 
##      4      7      3      4      2      2      7      3      7      5 
##    774    775    776    777    778    779    780    781    782    783 
##      3      6      5      4      2      2      3      1      3      4 
##    784    785    786    787    788    789    790    791    793    795 
##      5      3      1      5      1      3      2      8      2      3 
##    796    797    798    799    800    801    802    803    804    805 
##      2      2      1      2      7      1      2      2      8      7 
##    806    807    808    809    810    811    812    813    814    815 
##      3      2      2      5      5      1      1      1      7      5 
##    816    817    818    819    820    821    822    823    824    825 
##      2      2      3      2      4      2      5      3      2      1 
##    826    827    828    829    830    831    832    833    834    835 
##      1      1      1      5      4      1      4      1      4      4 
##    836    837    838    839    840    841    842    843    844    845 
##      2      3      3      3      5      3      7      1      2      7 
##    846    847    848    849    850    851    852    853    854    855 
##      4      1      3      3      6      4      2      3      2      7 
##    856    857    858    859    860    861    862    863    864    865 
##      3      2      2      3      1      5      6      1      6      3 
##    866    867    868    869    870    872    873    874    875    876 
##      2      1      2      4      6      4      3      3      5      5 
##    877    878    879    880    881    882    883    884    885    886 
##      2      1      3      5      2      3      3      4      3      5 
##    887    888    889    890    891    892    893    894    895    896 
##      8      2      1      6      3      2      4      2      6      3 
##    897    898    899    900    902    903    904    905    906    907 
##      3      5      1      4      4      2      3      4      2      2 
##    908    909    910    912    913    914    915    916    917    918 
##      1      2      1      5      2      1      2      2      7      4 
##    919    920    921    922    923    924    925    926    927    928 
##      3      1      2      3      2      3      2      3      4      3 
##    929    930    931    932    933    934    935    936    937    938 
##      1      2      7      6      2      5      1      5      2      4 
##    939    940    941    942    943    944    945    946    947    948 
##      2      2      3      2      2      1      2      4      3      2 
##    949    951    952    953    954    955    957    959    960    961 
##      4      3      3      1      2      2      2      5      5      2 
##    962    963    965    966    969    970    971    972    973    974 
##      2      1      1      1      4      1      4      3      1      1 
##    975    976    977    978    979    980    982    983    984    985 
##      2      7      3      2      1      3      2      2      2      3 
##    986    987    988    989    990    991    992    993    994    995 
##      1      1      2      2      1      1      5      2      4      4 
##    996    997    998    999   1000   1001   1002   1003   1004   1005 
##      4      3      5      1      2      4      4      5      4      2 
##   1006   1007   1008   1009   1010   1011   1012   1013   1014   1015 
##      3      1      3      2      6      7      3      3      3      1 
##   1016   1017   1018   1019   1020   1021   1022   1023   1024   1025 
##      4      2      4      1      1      3      1      3      4      2 
##   1026   1027   1028   1029   1030   1031   1032   1033   1034   1035 
##      6      2      3      3      1      2      3      1      3      3 
##   1037   1038   1039   1040   1042   1043   1044   1046   1047   1048 
##      2      1      4      1      2      1      3      1      3      2 
##   1049   1050   1051   1052   1053   1054   1055   1056   1057   1058 
##      2      3      1      2      1      3      2      5      2      3 
##   1059   1060   1061   1062   1063   1064   1066   1067   1068   1069 
##      2      3      3      3      1      4      6      4      2      2 
##   1070   1071   1072   1073   1074   1075   1077   1078   1079   1080 
##      3      4      3      4      4      2      2      4      1      2 
##   1081   1082   1083   1084   1086   1087   1088   1089   1090   1091 
##      1      3      1      7      1      3      2      1      5      4 
##   1092   1093   1094   1095   1096   1097   1098   1099   1100   1101 
##      2      1      6      6      3      2      2      3      2      2 
##   1102   1103   1104   1105   1106   1107   1108   1109   1110   1111 
##      5      5      3      6      1      4      5      2      5      2 
##   1112   1113   1114   1115   1116   1117   1118   1119   1120   1121 
##      5      1      1      3      3      2      2      6      1      4 
##   1122   1123   1124   1125   1126   1127   1129   1130   1132   1133 
##      3      1      3      2      6      4      3      4      3      3 
##   1134   1135   1136   1137   1138   1139   1140   1141   1142   1143 
##      3      1      3      4      2      2      6      1      5      2 
##   1144   1145   1146   1147   1148   1149   1150   1151   1152   1153 
##      2      1      3      1      4      1      2      1      2      1 
##   1154   1155   1156   1157   1159   1160   1161   1162   1164   1165 
##      2      8      5      1      2      3      3      3      4      3 
##   1166   1167   1168   1169   1170   1171   1172   1173   1174   1175 
##      4      1      1      1      2      4      5      2      5      5 
##   1176   1177   1178   1179   1180   1181   1183   1184   1185   1186 
##      3      3      5      3      5      5      4      1      1      3 
##   1187   1188   1189   1190   1192   1195   1196   1197   1198   1199 
##      2      4      2      1      5      1      2      2      1      3 
##   1200   1201   1202   1203   1205   1206   1207   1208   1209   1210 
##      2      3      3      1      4      1      7      1      1      3 
##   1211   1212   1213   1214   1215   1217   1218   1219   1220   1223 
##      3      7      1      4      3      3      3      4      3      1 
##   1224   1225   1226   1227   1228   1229   1231   1232   1233   1234 
##      3      3      1      6      3      5      1      2      3      7 
##   1235   1236   1238   1241   1242   1243   1244   1245   1246   1247 
##      4      2      4      2      3      2      2      4      2      5 
##   1248   1249   1250   1251   1252   1253   1254   1255   1257   1259 
##      1      1      6      2      3      2      1      3      2      3 
##   1260   1261   1262   1264   1265   1266   1267   1268   1269   1270 
##      5      4      3      3      2      2      4      1      1      6 
##   1271   1272   1273   1274   1275   1276   1277   1278   1279   1280 
##      2      2      1      2      3      1      1      2      2      1 
##   1281   1282   1283   1285   1286   1287   1288   1289   1290   1291 
##      3      3      4      3      2      4      1      4      1      1 
##   1292   1293   1294   1297   1299   1300   1301   1302   1303   1304 
##      2      5      1      2      1      3      2      4      2      2 
##   1305   1306   1307   1308   1309   1310   1311   1312   1313   1314 
##      4      1      3      3      1      2      2      2      3      4 
##   1315   1317   1318   1320   1321   1322   1323   1324   1325   1327 
##      2      1      2      2      1      4      1      1      2      3 
##   1328   1329   1331   1332   1333   1334   1335   1336   1337   1338 
##      1      2      2      1      6      2      4      1      1      1 
##   1339   1340   1341   1342   1343   1344   1345   1346   1347   1348 
##      2      2      1      2      2      6      1      5      2      3 
##   1349   1350   1351   1352   1353   1354   1355   1356   1358   1359 
##      2      2      1      1      2      3      3      3      5      2 
##   1360   1361   1363   1364   1365   1366   1368   1370   1372   1374 
##      2      2      2      2      3      2      3      6      2      4 
##   1375   1377   1378   1379   1380   1381   1382   1383   1384   1386 
##      1      1      3      1      2      6      1      1      3      3 
##   1387   1388   1390   1391   1392   1393   1395   1396   1397   1398 
##      2      2      2      2      1      1      2      2      1      2 
##   1399   1400   1401   1402   1404   1405   1406   1407   1408   1409 
##      3      1      2      1      2      3      2      1      1      3 
##   1410   1411   1412   1413   1414   1415   1416   1417   1418   1419 
##      1      2      2      3      1      4      2      1      1      2 
##   1421   1423   1424   1425   1426   1427   1429   1430   1431   1432 
##      2      3      2      6      4      3      1      1      5      4 
##   1433   1434   1435   1436   1437   1440   1441   1442   1444   1445 
##      2      3      1      2      1      2      2      3      2      2 
##   1446   1447   1448   1449   1450   1451   1454   1455   1458   1459 
##      1      4      1      2      3      2      3      1      2      4 
##   1460   1461   1462   1463   1464   1465   1466   1467   1468   1470 
##      1      2      3      3      6      1      5      2      1      1 
##   1471   1472   1473   1474   1475   1476   1477   1479   1480   1481 
##      1      5      3      1      1      2      2      2      6      4 
##   1483   1484   1485   1486   1487   1488   1490   1491   1493   1494 
##      1      3      1      1      1      3      2      2      3      1 
##   1495   1496   1497   1498   1499   1500   1501   1503   1504   1505 
##      4      3      1      2      2      8      3      1      2      3 
##   1509   1510   1511   1512   1513   1514   1515   1516   1517   1518 
##      3      1      2      3      3      1      1      2      2      5 
##   1520   1521   1522   1523   1525   1526   1528   1529   1530   1531 
##      1      1      3      4      1      1      1      1      2      1 
##   1532   1533   1534   1535   1536   1537   1538   1539   1540   1541 
##      2      2      1      2      4      1      2      1      1      2 
##   1542   1544   1546   1547   1548   1549   1550   1551   1552   1553 
##      2      2      1      2      1      3      2      2      1      3 
##   1554   1555   1556   1557   1558   1560   1561   1562   1563   1564 
##      1      1      3      2      4      2      1      1      2      3 
##   1565   1568   1569   1570   1571   1572   1573   1574   1575   1576 
##      3      4      5      4      1      1      2      2      2      2 
##   1577   1578   1582   1583   1584   1585   1586   1587   1588   1589 
##      1      3      2      6      2      2      1      1      2      2 
##   1590   1592   1593   1594   1596   1597   1598   1599   1600   1601 
##      2      1      4      1      2      5      2      3      3      1 
##   1602   1603   1605   1606   1607   1608   1609   1611   1612   1613 
##      4      4      1      2      1      1      2      2      2      2 
##   1614   1615   1617   1619   1620   1622   1623   1624   1625   1627 
##      1      2      2      4      6      1      5      1      2      1 
##   1628   1629   1630   1631   1632   1633   1634   1635   1636   1638 
##      1      1      3      2      4      1      4      1      3      2 
##   1640   1641   1642   1643   1644   1645   1646   1647   1648   1650 
##      4      2      2      1      1      1      1      1      2      5 
##   1651   1652   1653   1655   1656   1657   1659   1660   1661   1662 
##      1      1      2      5      2      3      1      5      1      2 
##   1663   1665   1666   1667   1668   1670   1671   1673   1674   1675 
##      1      2      2      3      2      4      2      3      3      2 
##   1676   1678   1679   1680   1681   1684   1685   1687   1688   1689 
##      1      4      1      3      2      2      1      2      1      3 
##   1690   1694   1695   1697   1698   1699   1700   1701   1702   1703 
##      2      1      3      1      2      1      1      1      1      2 
##   1704   1705   1706   1707   1708   1709   1711   1712   1714   1716 
##      4      1      3      1      1      1      1      1      2      3 
##   1717   1718   1719   1720   1721   1723   1724   1725   1726   1727 
##      1      1      1      2      2      2      3      1      3      2 
##   1728   1729   1730   1731   1733   1734   1735   1736   1737   1738 
##      2      2      1      1      1      1      1      1      1      4 
##   1739   1740   1741   1742   1743   1744   1745   1746   1747   1749 
##      1      1      2      2      1      1      3      1      2      2 
##   1750   1754   1756   1758   1760   1761   1762   1764   1765   1766 
##      2      2      1      4      2      1      1      2      1      3 
##   1767   1768   1769   1770   1771   1773   1774   1775   1776   1778 
##      1      1      1      1      1      2      2      6      1      2 
##   1779   1780   1781   1782   1783   1784   1785   1786   1787   1790 
##      1      5      4      1      2      1      1      1      1      1 
##   1791   1792   1794   1795   1796   1797   1799   1800   1801   1802 
##      1      4      2      4      2      1      1      5      2      2 
##   1803   1804   1805   1806   1809   1810   1811   1812   1813   1814 
##      1      1      4      1      1      2      2      3      3      1 
##   1816   1817   1818   1820   1821   1822   1823   1824   1825   1826 
##      4      2      2      1      2      4      1      5      4      2 
##   1827   1828   1829   1830   1831   1832   1834   1835   1836   1837 
##      2      2      3      1      1      1      1      1      5      2 
##   1838   1839   1840   1841   1842   1844   1845   1846   1847   1848 
##      2      3      3      1      1      1      1      1      2      1 
##   1849   1850   1851   1852   1853   1854   1856   1860   1861   1862 
##      1      1      1      2      2      2      1      2      2      4 
##   1863   1864   1865   1866   1867   1868   1870   1872   1873   1874 
##      1      1      1      1      1      2      2      2      3      2 
##   1875   1877   1878   1879   1881   1882   1883   1885   1886   1887 
##      2      3      1      3      3      2      1      4      1      1 
##   1889   1890   1891   1892   1895   1896   1898   1899   1901   1902 
##      3      2      4      2      3      2      1      3      3      1 
##   1903   1904   1905   1906   1907   1908   1909   1911   1913   1914 
##      2      2      1      1      1      3      1      1      1      1 
##   1915   1916   1917   1918   1919   1920   1924   1925   1926   1929 
##      1      1      1      1      2      2      3      1      2      1 
##   1930   1931   1932   1933   1934   1935   1937   1938   1939   1941 
##      2      1      2      3      2      3      1      2      1      1 
##   1942   1943   1944   1946   1947   1949   1951   1952   1953   1954 
##      3      1      2      2      3      4      2      1      1      2 
##   1955   1956   1957   1958   1960   1961   1963   1965   1966   1969 
##      1      1      1      1      4      3      1      1      2      1 
##   1973   1974   1975   1977   1979   1980   1981   1982   1983   1985 
##      1      1      1      1      1      2      3      1      1      2 
##   1986   1989   1990   1991   1993   1998   2001   2002   2003   2006 
##      1      1      1      3      1      1      2      2      3      1 
##   2007   2008   2011   2012   2013   2015   2016   2017   2018   2021 
##      5      3      1      2      2      5      2      3      1      2 
##   2022   2023   2024   2025   2026   2027   2028   2029   2030   2031 
##      2      1      1      2      1      3      2      2      1      2 
##   2032   2033   2034   2036   2037   2038   2040   2041   2042   2043 
##      1      1      3      1      1      3      2      2      1      3 
##   2044   2045   2046   2047   2049   2050   2051   2052   2054   2055 
##      1      1      2      5      2      3      4      1      1      1 
##   2056   2057   2060   2061   2064   2065   2066   2067   2069   2071 
##      2      1      3      1      1      2      1      2      1      1 
##   2072   2073   2074   2075   2076   2078   2079   2081   2082   2083 
##      1      3      2      1      2      2      2      4      1      2 
##   2084   2086   2090   2091   2092   2099   2100   2101   2102   2104 
##      3      1      2      2      2      2      3      2      1      2 
##   2107   2110   2111   2113   2114   2116   2117   2118   2119   2120 
##      1      1      2      2      3      1      2      1      1      1 
##   2121   2122   2123   2124   2125   2126   2127   2129   2130   2131 
##      2      3      1      1      1      1      3      1      1      1 
##   2133   2135   2137   2138   2141   2142   2143   2145   2146   2147 
##      3      1      2      1      2      1      1      1      1      1 
##   2148   2150   2152   2153   2154   2156   2157   2159   2160   2161 
##      2      1      1      2      2      1      1      3      1      2 
##   2164   2165   2166   2169   2170   2171   2174   2175   2177   2178 
##      2      1      1      1      1      1      2      2      1      2 
##   2180   2181   2182   2184   2185   2186   2188   2189   2190   2191 
##      1      1      1      1      1      2      1      2      1      2 
##   2193   2194   2195   2197   2198   2200   2202   2203   2205   2206 
##      2      1      1      1      1      1      3      1      1      2 
##   2207   2208   2211   2212   2213   2214   2215   2216   2218   2219 
##      1      2      1      3      2      1      1      2      1      2 
##   2220   2221   2222   2224   2225   2226   2227   2228   2229   2230 
##      1      2      1      2      1      1      3      2      1      1 
##   2233   2237   2238   2240   2243   2244   2249   2250   2251   2252 
##      1      2      2      1      1      2      1      3      1      2 
##   2253   2254   2255   2260   2261   2262   2264   2268   2269   2270 
##      1      2      2      1      2      2      2      2      1      1 
##   2271   2272   2273   2274   2275   2278   2279   2281   2282   2283 
##      1      1      2      2      2      2      4      1      1      2 
##   2285   2286   2287   2288   2289   2290   2291   2292   2293   2294 
##      3      2      1      2      3      2      2      1      1      1 
##   2295   2296   2298   2300   2301   2302   2303   2304   2305   2306 
##      2      2      4      1      1      1      2      2      2      1 
##   2307   2308   2309   2310   2311   2313   2316   2317   2318   2320 
##      1      3      1      1      1      1      3      1      1      2 
##   2321   2322   2325   2326   2328   2329   2331   2334   2336   2337 
##      1      3      1      1      1      2      1      2      2      3 
##   2340   2341   2343   2345   2346   2347   2348   2349   2352   2353 
##      1      1      2      2      1      2      1      1      2      4 
##   2354   2356   2358   2360   2361   2362   2363   2364   2366   2367 
##      2      1      2      3      2      1      1      1      2      1 
##   2368   2369   2370   2371   2372   2373   2374   2376   2377   2381 
##      2      3      2      2      1      2      1      1      1      1 
##   2383   2384   2385   2386   2387   2389   2390   2391   2392   2394 
##      3      1      3      1      2      1      1      3      1      2 
##   2396   2397   2398   2399   2400   2403   2404   2405   2410   2411 
##      2      2      1      1      1      2      3      4      4      1 
##   2415   2416   2419   2420   2421   2422   2424   2426   2428   2429 
##      1      4      1      1      1      3      1      1      2      1 
##   2430   2431   2432   2433   2434   2435   2436   2438   2441   2442 
##      1      2      1      1      3      1      1      1      2      1 
##   2444   2445   2447   2450   2451   2453   2456   2457   2458   2459 
##      1      2      1      1      1      1      1      2      1      3 
##   2460   2463   2464   2466   2467   2468   2469   2471   2476   2478 
##      1      2      2      1      2      1      2      1      2      3 
##   2479   2480   2481   2482   2483   2485   2488   2489   2491   2495 
##      1      3      1      1      1      2      1      4      1      1 
##   2497   2499   2500   2502   2504   2505   2506   2508   2509   2511 
##      1      1      3      1      1      1      3      1      1      1 
##   2512   2513   2514   2515   2516   2518   2523   2524   2525   2526 
##      2      1      1      1      1      2      1      2      1      1 
##   2527   2530   2531   2532   2533   2534   2535   2536   2538   2539 
##      1      3      1      2      1      1      4      1      1      1 
##   2540   2541   2542   2543   2544   2546   2548   2549   2550   2553 
##      2      1      2      1      1      2      1      1      4      3 
##   2554   2555   2556   2557   2558   2559   2561   2562   2564   2565 
##      2      2      1      3      2      1      1      2      1      3 
##   2566   2567   2569   2570   2571   2572   2573   2574   2575   2578 
##      1      2      1      1      3      3      3      1      1      2 
##   2579   2580   2582   2583   2584   2586   2587   2588   2589   2590 
##      1      3      1      2      3      1      1      1      1      2 
##   2591   2593   2595   2597   2598   2600   2601   2602   2603   2605 
##      3      2      1      3      3      4      3      2      1      2 
##   2606   2607   2608   2609   2611   2612   2613   2617   2618   2620 
##      1      1      1      1      1      1      1      1      1      1 
##   2621   2624   2628   2629   2630   2631   2632   2633   2634   2635 
##      2      1      2      1      1      2      1      3      1      2 
##   2638   2640   2641   2643   2644   2646   2647   2648   2650   2651 
##      1      1      1      1      1      1      2      1      1      1 
##   2653   2654   2656   2658   2659   2660   2661   2662   2664   2666 
##      1      2      2      2      1      1      2      1      1      1 
##   2667   2670   2677   2678   2679   2681   2682   2683   2684   2685 
##      1      1      1      1      2      1      2      1      4      3 
##   2686   2687   2691   2695   2696   2697   2699   2700   2701   2703 
##      1      4      2      1      3      2      1      2      1      1 
##   2705   2706   2707   2708   2709   2710   2711   2712   2713   2715 
##      3      1      1      1      1      1      1      1      2      2 
##   2717   2719   2720   2723   2724   2726   2727   2728   2729   2730 
##      1      1      1      3      1      1      1      2      1      2 
##   2732   2735   2737   2739   2742   2744   2746   2747   2750   2751 
##      2      2      2      1      3      2      1      2      3      1 
##   2753   2754   2755   2756   2757   2758   2759   2765   2766   2767 
##      1      1      2      1      4      2      3      2      2      2 
##   2768   2769   2770   2772   2773   2774   2775   2776   2777   2778 
##      1      1      1      2      1      1      1      2      1      1 
##   2779   2782   2783   2784   2786   2787   2788   2790   2791   2792 
##      2      2      1      2      3      1      1      1      1      3 
##   2794   2795   2796   2797   2798   2800   2801   2802   2804   2806 
##      1      1      1      1      1      2      3      1      1      1 
##   2807   2808   2809   2811   2812   2814   2815   2817   2818   2819 
##      1      2      3      1      1      1      1      4      1      1 
##   2820   2821   2822   2823   2824   2825   2826   2827   2828   2829 
##      2      2      3      1      1      1      2      3      5      2 
##   2831   2832   2835   2836   2839   2840   2841   2844   2845   2846 
##      1      1      2      1      1      1      2      2      2      1 
##   2849   2850   2851   2852   2853   2855   2856   2858   2859   2860 
##      3      1      1      2      3      1      1      1      1      2 
##   2861   2862   2863   2866   2868   2869   2870   2874   2876   2877 
##      1      2      1      1      1      1      1      3      3      5 
##   2880   2881   2883   2884   2885   2886   2888   2892   2896   2897 
##      2      1      1      1      3      1      1      1      1      2 
##   2898   2900   2901   2903   2904   2909   2910   2914   2915   2917 
##      1      2      1      2      1      1      1      1      2      2 
##   2919   2921   2922   2923   2924   2926   2927   2931   2933   2936 
##      1      1      1      2      2      3      1      1      1      1 
##   2938   2940   2942   2947   2948   2949   2950   2951   2952   2953 
##      2      1      1      1      1      1      1      3      2      1 
##   2954   2956   2957   2961   2963   2964   2965   2969   2970   2971 
##      1      1      1      1      1      1      1      2      1      1 
##   2974   2975   2980   2982   2983   2984   2986   2987   2988   2989 
##      2      2      2      1      1      1      1      1      2      1 
##   2990   2992   2993   2994   2996   2997   2998   3000   3001   3002 
##      1      1      3      1      2      2      1      2      1      1 
##   3003   3004   3005   3006   3008   3010   3012   3013   3014   3015 
##      1      1      1      1      1      1      1      1      1      2 
##   3016   3021   3025   3026   3028   3030   3034   3035   3036   3037 
##      2      1      2      2      2      1      1      1      2      2 
##   3038   3040   3042   3044   3045   3046   3048   3054   3055   3056 
##      1      1      1      2      2      1      1      2      1      2 
##   3057   3058   3060   3061   3062   3064   3066   3068   3070   3071 
##      1      1      1      2      1      1      2      1      2      2 
##   3072   3073   3077   3078   3079   3080   3084   3085   3090   3093 
##      1      1      1      1      3      1      2      1      1      2 
##   3096   3098   3099   3100   3103   3105   3109   3110   3111   3114 
##      2      1      1      2      2      3      3      1      3      3 
##   3117   3118   3120   3121   3125   3126   3127   3128   3130   3132 
##      1      2      1      1      2      1      3      1      2      3 
##   3134   3135   3136   3137   3138   3140   3145   3147   3150   3151 
##      1      1      1      2      2      2      2      1      2      1 
##   3152   3157   3158   3161   3162   3163   3164   3165   3167   3168 
##      1      1      1      1      1      1      1      1      2      1 
##   3170   3172   3175   3178   3180   3181   3183   3184   3186   3187 
##      1      1      1      1      1      1      1      1      2      1 
##   3188   3191   3192   3193   3194   3197   3198   3202   3204   3206 
##      4      1      1      2      1      2      1      1      1      1 
##   3207   3208   3212   3214   3215   3217   3219   3222   3223   3224 
##      2      1      1      3      2      1      1      3      1      1 
##   3225   3226   3227   3231   3232   3233   3235   3236   3237   3238 
##      1      2      1      1      2      1      1      3      1      2 
##   3239   3240   3241   3245   3246   3249   3251   3253   3254   3256 
##      1      1      1      1      1      1      1      1      1      1 
##   3258   3259   3260   3261   3263   3265   3268   3269   3272   3273 
##      2      1      1      2      1      1      1      1      1      2 
##   3277   3278   3279   3281   3282   3283   3284   3285   3287   3288 
##      1      2      2      1      1      1      2      2      1      2 
##   3289   3291   3294   3295   3296   3298   3301   3303   3304   3306 
##      1      1      1      1      2      1      1      1      1      1 
##   3307   3308   3311   3313   3314   3317   3318   3319   3321   3322 
##      1      1      1      1      1      1      2      1      1      1 
##   3323   3328   3329   3330   3331   3332   3336   3337   3342   3347 
##      2      1      1      3      1      1      1      2      1      1 
##   3349   3350   3352   3356   3358   3359   3360   3365   3368   3369 
##      1      1      1      2      1      2      3      1      2      1 
##   3370   3375   3378   3379   3380   3382   3383   3384   3386   3388 
##      1      2      1      2      1      1      2      2      1      1 
##   3391   3394   3395   3396   3399   3400   3401   3402   3403   3404 
##      1      2      2      1      1      2      1      1      1      1 
##   3405   3407   3408   3411   3414   3416   3419   3420   3423   3424 
##      3      1      1      1      1      1      2      3      1      2 
##   3425   3427   3428   3430   3432   3433   3435   3436   3437   3440 
##      1      2      1      1      3      2      2      1      1      2 
##   3441   3442   3443   3444   3445   3450   3452   3454   3455   3456 
##      3      1      1      2      3      3      1      1      1      2 
##   3459   3460   3461   3464   3466   3467   3468   3471   3472   3473 
##      1      1      1      2      1      2      1      2      1      1 
##   3474   3475   3477   3478   3479   3481   3482   3483   3484   3485 
##      1      2      2      2      3      1      1      2      1      1 
##   3489   3494   3495   3496   3499   3500   3507   3511   3516   3517 
##      1      1      1      1      2      2      2      1      1      1 
##   3520   3522   3525   3527   3528   3529   3531   3534   3535   3536 
##      1      2      1      1      1      1      1      2      1      3 
##   3537   3539   3541   3542   3543   3544   3547   3550   3551   3552 
##      1      2      2      1      3      1      1      3      1      1 
##   3553   3555   3557   3560   3561   3562   3564   3571   3572   3575 
##      2      1      1      2      1      1      1      2      4      3 
##   3576   3577   3578   3580   3581   3582   3585   3586   3590   3594 
##      1      1      1      1      1      1      1      1      2      1 
##   3597   3599   3600   3603   3604   3606   3608   3609   3610   3613 
##      2      1      2      3      1      1      2      1      2      1 
##   3614   3615   3617   3619   3622   3623   3626   3627   3631   3632 
##      1      1      1      1      1      2      3      2      1      1 
##   3633   3634   3637   3638   3639   3640   3642   3644   3648   3650 
##      2      1      1      1      1      1      1      1      1      2 
##   3651   3658   3659   3660   3661   3663   3665   3666   3668   3670 
##      3      1      1      1      1      1      2      1      1      2 
##   3671   3672   3674   3676   3677   3678   3681   3682   3683   3686 
##      1      2      2      1      1      1      1      1      1      1 
##   3687   3688   3690   3691   3697   3698   3699   3700   3702   3703 
##      1      1      1      1      1      1      1      2      3      2 
##   3705   3706   3707   3708   3712   3713   3714   3715   3716   3717 
##      1      1      1      1      1      1      2      2      1      2 
##   3720   3724   3725   3726   3730   3731   3733   3735   3738   3742 
##      3      1      2      1      1      2      1      1      1      2 
##   3745   3746   3751   3754   3756   3758   3764   3766   3769   3771 
##      1      1      1      3      1      2      1      1      5      1 
##   3773   3776   3780   3784   3786   3787   3788   3791   3797   3801 
##      1      1      2      1      2      1      2      1      1      1 
##   3804   3806   3809   3811   3813   3814   3815   3818   3820   3821 
##      1      1      2      2      2      2      1      2      1      1 
##   3822   3825   3830   3831   3832   3842   3843   3846   3847   3849 
##      1      1      1      1      1      1      1      1      1      1 
##   3850   3851   3853   3860   3861   3862   3867   3868   3870   3871 
##      1      1      1      1      1      2      3      1      1      1 
##   3873   3875   3882   3886   3887   3888   3889   3890   3893   3894 
##      2      2      1      1      1      1      1      1      1      1 
##   3896   3900   3901   3904   3906   3907   3908   3913   3914   3918 
##      1      1      1      1      1      2      2      2      2      1 
##   3919   3920   3921   3926   3929   3930   3931   3932   3933   3935 
##      1      2      2      1      3      1      1      1      1      1 
##   3936   3937   3938   3939   3940   3941   3942   3947   3948   3949 
##      2      1      1      1      1      2      1      1      2      1 
##   3952   3953   3954   3956   3957   3960   3965   3966   3969   3971 
##      2      1      1      3      1      1      1      1      2      1 
##   3976   3979   3980   3985   3986   3987   3990   3991   3992   3995 
##      3      1      1      1      1      1      1      2      1      1 
##   3996   4000   4001   4002   4006   4007   4008   4009   4010   4012 
##      2      2      1      1      1      1      1      1      1      3 
##   4014   4016   4019   4022   4023   4024   4025   4026   4027   4033 
##      1      1      1      2      1      1      1      1      2      1 
##   4034   4036   4040   4041   4042   4044   4047   4049   4050   4051 
##      1      3      2      2      1      1      2      1      1      2 
##   4052   4054   4055   4056   4060   4063   4067   4071   4074   4075 
##      1      2      1      2      2      1      1      1      1      1 
##   4076   4077   4079   4080   4081   4082   4084   4086   4090   4091 
##      1      1      1      2      1      1      2      1      1      1 
##   4096   4097   4098   4106   4107   4109   4113   4117   4119   4124 
##      1      2      1      2      1      1      1      1      1      1 
##   4125   4127   4128   4129   4130   4131   4135   4138   4145   4147 
##      1      2      3      1      1      1      1      1      3      1 
##   4148   4149   4150   4153   4154   4157   4164   4166   4167   4168 
##      1      3      1      1      2      1      2      1      1      1 
##   4171   4172   4173   4174   4176   4177   4179   4180   4182   4185 
##      4      2      4      2      1      1      1      1      1      2 
##   4192   4195   4196   4203   4205   4209   4210   4212   4214   4215 
##      1      1      2      2      3      2      1      1      2      1 
##   4217   4219   4223   4229   4231   4232   4235   4236   4238   4239 
##      1      2      2      3      1      1      2      1      1      1 
##   4240   4245   4250   4251   4255   4256   4257   4258   4259   4261 
##      2      1      1      2      2      1      2      1      1      2 
##   4262   4263   4265   4266   4267   4269   4270   4271   4273   4280 
##      1      1      1      1      2      2      1      1      3      1 
##   4286   4288   4289   4291   4292   4295   4297   4298   4299   4300 
##      1      2      1      1      1      1      1      1      1      1 
##   4301   4306   4310   4311   4313   4317   4318   4319   4320   4321 
##      1      2      3      1      1      2      1      1      1      1 
##   4322   4323   4325   4326   4327   4328   4329   4331   4335   4336 
##      1      3      1      1      1      2      1      1      1      1 
##   4339   4340   4341   4348   4351   4356   4357   4363   4365   4369 
##      2      2      1      1      1      5      2      1      1      1 
##   4371   4375   4376   4378   4382   4386   4388   4391   4393   4398 
##      1      1      1      1      1      1      1      2      1      1 
##   4400   4403   4407   4409   4410   4411   4413   4414   4420   4422 
##      1      1      1      2      2      2      1      1      2      1 
##   4423   4425   4429   4430   4431   4432   4434   4435   4437   4439 
##      2      3      3      2      1      1      1      1      1      1 
##   4440   4441   4442   4443   4444   4445   4451   4453   4457   4458 
##      1      1      1      1      2      1      2      1      1      1 
##   4459   4461   4462   4465   4468   4469   4477   4481   4485   4486 
##      1      2      1      1      1      1      1      1      2      2 
##   4490   4495   4496   4497   4498   4500   4501   4502   4503   4508 
##      1      2      1      2      2      1      2      1      1      1 
##   4511   4513   4514   4518   4519   4520   4522   4523   4529   4535 
##      1      1      1      1      1      1      1      1      1      1 
##   4540   4545   4551   4554   4556   4558   4560   4562   4563   4566 
##      2      1      1      3      1      1      1      1      1      1 
##   4572   4579   4580   4581   4584   4586   4587   4591   4594   4595 
##      1      3      1      2      3      1      1      1      2      1 
##   4597   4600   4603   4604   4605   4608   4609   4611   4612   4618 
##      1      1      1      3      1      2      2      1      1      1 
##   4621   4622   4624   4627   4630   4632   4633   4634   4636   4643 
##      1      1      1      2      2      1      1      1      2      1 
##   4649   4650   4651   4655   4659   4661   4663   4666   4667   4671 
##      1      4      2      1      1      1      1      1      3      1 
##   4672   4675   4679   4681   4682   4685   4686   4693   4697   4700 
##      1      1      2      1      1      1      2      1      1      1 
##   4702   4703   4705   4706   4708   4709   4712   4714   4715   4716 
##      1      1      1      1      1      2      1      1      1      1 
##   4717   4719   4720   4721   4723   4725   4727   4728   4730   4733 
##      1      1      1      1      1      1      1      1      1      1 
##   4740   4742   4743   4745   4747   4749   4750   4751   4756   4757 
##      1      1      2      1      1      1      1      2      1      3 
##   4762   4763   4766   4768   4770   4773   4776   4777   4783   4787 
##      1      1      1      1      1      2      1      2      1      2 
##   4789   4792   4793   4794   4797   4803   4804   4806   4814   4818 
##      1      1      1      1      1      1      1      1      1      1 
##   4819   4820   4823   4827   4831   4832   4837   4840   4841   4842 
##      1      2      1      2      1      2      1      1      1      1 
##   4843   4846   4847   4848   4850   4855   4858   4859   4860   4861 
##      1      2      1      1      2      1      1      1      1      1 
##   4863   4871   4874   4878   4882   4885   4887   4890   4894   4895 
##      1      1      1      1      2      1      1      2      2      1 
##   4897   4901   4904   4905   4908   4916   4917   4921   4930   4931 
##      1      1      1      1      2      1      1      1      1      1 
##   4936   4940   4941   4943   4944   4946   4951   4955   4959   4962 
##      1      1      1      1      1      2      2      1      1      1 
##   4966   4968   4980   4981   4983   4984   4985   4986   4987   4990 
##      1      1      1      1      1      2      1      1      1      1 
##   4994   4996   5000   5001   5003   5005   5006   5007   5010   5014 
##      1      1      3      2      1      2      2      1      1      1 
##   5015   5016   5019   5020   5021   5022   5023   5027   5028   5029 
##      1      3      1      1      1      1      2      3      3      1 
##   5031   5038   5039   5044   5045   5049   5050   5051   5052   5053 
##      1      1      1      1      2      1      1      2      1      1 
##   5055   5061   5062   5065   5068   5075   5078   5081   5084   5088 
##      1      2      1      1      2      1      1      1      2      2 
##   5090   5095   5097   5102   5105   5106   5108   5114   5117   5118 
##      1      2      1      1      1      1      1      2      1      1 
##   5120   5122   5126   5129   5130   5132   5133   5134   5136   5137 
##      3      2      1      1      1      1      1      1      1      1 
##   5138   5140   5147   5148   5149   5150   5152   5153   5156   5157 
##      1      1      2      2      1      1      1      2      1      1 
##   5158   5165   5171   5173   5177   5178   5179   5183   5184   5185 
##      2      1      1      1      1      1      1      1      1      2 
##   5190   5191   5193   5194   5196   5200   5203   5205   5210   5214 
##      2      1      2      1      1      1      1      1      1      2 
##   5221   5223   5229   5240   5245   5246   5247   5248   5253   5254 
##      1      1      1      1      1      1      1      1      1      1 
##   5256   5257   5263   5264   5265   5266   5267   5271   5272   5275 
##      1      1      1      1      1      1      1      1      1      1 
##   5284   5287   5289   5294   5296   5298   5299   5300   5303   5309 
##      1      2      2      1      3      2      1      1      1      1 
##   5315   5318   5321   5322   5323   5326   5328   5333   5336   5342 
##      1      2      1      3      1      2      1      1      2      2 
##   5343   5344   5345   5346   5347   5348   5349   5352   5353   5354 
##      2      1      2      1      1      1      2      1      1      1 
##   5355   5356   5358   5361   5365   5370   5371   5375   5381   5389 
##      1      1      2      3      1      1      2      2      2      1 
##   5391   5394   5396   5397   5402   5405   5407   5409   5414   5416 
##      1      1      1      1      5      1      1      1      1      1 
##   5417   5418   5419   5421   5422   5427   5428   5429   5431   5434 
##      1      1      2      1      1      1      3      1      1      1 
##   5436   5437   5438   5446   5454   5456   5460   5462   5469   5470 
##      1      1      2      1      1      2      1      1      1      1 
##   5473   5474   5477   5482   5487   5488   5491   5492   5494   5495 
##      1      2      1      1      3      1      1      1      1      1 
##   5498   5499   5503   5504   5505   5512   5513   5514   5515   5516 
##      1      2      1      1      1      1      1      1      1      1 
##   5517   5520   5521   5522   5528   5531   5533   5534   5536   5537 
##      3      1      1      1      1      1      1      1      1      1 
##   5538   5541   5542   5546   5549   5552   5554   5560   5561   5562 
##      1      1      1      2      2      1      1      1      1      1 
##   5564   5570   5571   5572   5574   5575   5577   5581   5582   5583 
##      1      1      2      1      1      3      1      1      1      3 
##   5590   5595   5600   5601   5602   5604   5605   5607   5608   5614 
##      2      2      2      1      1      1      1      1      1      1 
##   5616   5627   5629   5633   5635   5639   5647   5650   5653   5654 
##      1      2      1      1      1      1      1      1      1      1 
##   5655   5661   5662   5665   5669   5678   5685   5687   5688   5690 
##      2      1      1      1      1      1      2      1      2      2 
##   5691   5695   5697   5703   5704   5708   5710   5711   5714   5715 
##      1      1      1      2      2      1      1      1      1      1 
##   5717   5718   5720   5722   5723   5724   5727   5730   5731   5732 
##      1      1      1      1      1      2      2      3      1      1 
##   5736   5740   5746   5754   5760   5763   5765   5776   5779   5782 
##      1      1      1      2      1      2      1      1      1      1 
##   5783   5785   5788   5795   5796   5797   5800   5804   5805   5811 
##      1      2      1      1      1      1      1      1      1      1 
##   5819   5822   5823   5830   5834   5835   5836   5838   5842   5844 
##      1      1      1      1      1      1      1      1      1      1 
##   5845   5846   5848   5849   5853   5854   5857   5859   5866   5867 
##      2      1      2      1      2      1      1      1      1      1 
##   5868   5874   5875   5877   5879   5881   5882   5886   5894   5895 
##      1      1      1      1      1      1      1      1      1      1 
##   5902   5904   5907   5908   5913   5917   5919   5922   5924   5927 
##      1      3      1      1      1      1      1      1      1      1 
##   5930   5935   5936   5938   5944   5947   5948   5956   5958   5961 
##      1      1      1      1      1      1      1      1      1      2 
##   5962   5963   5976   5979   5980   5981   5982   5984   5986   5990 
##      1      2      2      1      1      1      1      1      2      1 
##   5992   5996   5997   5998   6003   6004   6009   6011   6015   6016 
##      2      1      1      1      2      1      2      2      2      1 
##   6026   6029   6031   6034   6039   6042   6043   6046   6055   6056 
##      1      3      1      1      1      1      1      1      2      1 
##   6057   6059   6062   6063   6068   6069   6082   6085   6087   6089 
##      1      1      1      1      1      1      1      1      1      1 
##   6090   6092   6097   6105   6109   6114   6123   6127   6128   6129 
##      1      1      3      1      1      1      2      1      1      1 
##   6132   6136   6138   6143   6149   6151   6154   6156   6166   6170 
##      1      1      1      1      2      1      1      2      1      2 
##   6172   6174   6175   6177   6179   6188   6189   6195   6198   6200 
##      1      1      1      1      1      2      2      1      1      1 
##   6202   6203   6204   6206   6211   6214   6215   6222   6223   6226 
##      1      1      3      1      1      1      1      1      2      1 
##   6230   6234   6235   6237   6238   6239   6253   6256   6265   6266 
##      1      1      4      1      1      1      1      1      1      1 
##   6267   6271   6272   6274   6277   6280   6288   6295   6296   6297 
##      1      1      1      1      1      1      1      1      1      1 
##   6299   6304   6307   6309   6312   6314   6317   6321   6325   6333 
##      1      1      1      1      1      1      1      1      1      1 
##   6336   6338   6339   6340   6343   6344   6345   6353   6355   6357 
##      1      1      1      1      1      1      1      1      2      1 
##   6360   6371   6372   6377   6384   6386   6387   6388   6389   6391 
##      1      1      2      2      1      2      2      1      1      1 
##   6393   6397   6398   6403   6404   6407   6413   6418   6423   6424 
##      1      1      1      1      1      1      1      1      1      2 
##   6426   6431   6437   6438   6439   6440   6442   6450   6451   6453 
##      2      1      1      1      1      3      1      1      1      1 
##   6458   6460   6461   6465   6466   6476   6478   6482   6485   6490 
##      1      4      1      1      1      2      1      1      1      1 
##   6493   6497   6498   6500   6501   6507   6511   6515   6516   6520 
##      1      1      1      1      1      1      1      2      2      1 
##   6530   6534   6536   6540   6547   6551   6554   6557   6558   6560 
##      1      1      1      2      1      3      1      1      1      2 
##   6569   6581   6582   6584   6585   6586   6589   6592   6594   6611 
##      1      2      1      1      1      2      1      1      1      1 
##   6614   6615   6619   6621   6625   6632   6644   6645   6646   6648 
##      1      1      2      1      1      2      1      1      1      1 
##   6652   6653   6654   6658   6660   6661   6664   6676   6683   6691 
##      1      1      1      2      2      1      1      1      1      1 
##   6692   6699   6700   6703   6704   6707   6715   6717   6725   6728 
##      1      1      1      1      1      1      1      2      1      1 
##   6730   6731   6733   6734   6736   6742   6746   6748   6749   6750 
##      1      1      1      1      1      1      2      1      1      1 
##   6751   6753   6755   6762   6763   6767   6768   6770   6775   6777 
##      1      1      1      2      1      1      2      1      1      1 
##   6779   6782   6784   6786   6787   6788   6791   6792   6796   6799 
##      3      1      1      1      1      1      1      1      2      1 
##   6801   6802   6809   6819   6820   6822   6823   6842   6846   6851 
##      2      1      2      2      1      1      1      1      1      1 
##   6857   6863   6870   6875   6876   6878   6887   6891   6895   6896 
##      1      2      1      3      1      1      1      1      1      1 
##   6897   6909   6925   6926   6928   6931   6933   6934   6937   6940 
##      1      2      1      1      1      1      1      2      1      1 
##   6942   6943   6944   6949   6952   6954   6957   6959   6960   6973 
##      2      1      1      2      1      1      1      1      1      1 
##   6978   6980   6983   7000   7006   7009   7010   7011   7012   7017 
##      1      1      1      1      1      1      1      1      1      1 
##   7018   7019   7025   7026   7030   7034   7035   7041   7042   7044 
##      1      1      1      1      1      1      2      1      1      1 
##   7045   7053   7054   7061   7063   7065   7075   7078   7080   7081 
##      1      1      1      1      1      1      2      2      1      1 
##   7092   7093   7096   7097   7098   7101   7105   7112   7121   7122 
##      1      3      2      2      1      1      1      1      1      1 
##   7126   7132   7134   7137   7141   7144   7149   7150   7163   7165 
##      3      1      1      2      2      1      1      1      1      1 
##   7173   7181   7184   7189   7196   7205   7207   7213   7215   7223 
##      1      1      1      1      1      1      1      3      1      1 
##   7227   7229   7235   7240   7250   7262   7266   7268   7273   7274 
##      1      1      1      1      2      2      1      1      1      2 
##   7275   7280   7282   7287   7294   7300   7301   7302   7305   7306 
##      1      1      1      1      1      1      1      1      1      2 
##   7307   7308   7311   7312   7313   7316   7321   7323   7324   7325 
##      1      1      1      2      1      1      1      1      1      3 
##   7330   7337   7338   7342   7344   7347   7348   7356   7359   7365 
##      1      1      2      1      1      1      1      1      1      2 
##   7374   7376   7377   7378   7384   7393   7395   7396   7399   7400 
##      1      1      1      2      1      1      1      1      1      2 
##   7403   7404   7405   7413   7415   7419   7420   7422   7431   7433 
##      1      1      1      1      1      1      3      1      1      1 
##   7438   7439   7447   7452   7455   7456   7457   7458   7461   7463 
##      2      2      1      1      2      1      1      1      1      2 
##   7471   7474   7475   7481   7482   7484   7486   7488   7494   7496 
##      1      2      1      1      1      2      2      1      1      1 
##   7499   7501   7507   7510   7514   7522   7523   7524   7531   7538 
##      1      3      1      1      1      1      2      1      1      2 
##   7540   7543   7550   7551   7556   7561   7563   7566   7573   7579 
##      1      2      4      1      1      1      1      1      1      1 
##   7583   7595   7597   7598   7604   7605   7608   7626   7627   7642 
##      1      1      1      1      1      2      1      1      2      1 
##   7643   7644   7657   7659   7661   7662   7671   7672   7682   7684 
##      1      1      1      3      1      2      1      1      1      1 
##   7693   7694   7698   7702   7704   7712   7719   7720   7730   7733 
##      1      1      2      1      3      1      1      1      1      2 
##   7742   7744   7748   7750   7752   7756   7762   7766   7768   7769 
##      1      1      1      3      2      1      1      1      1      1 
##   7773   7775   7779   7786   7787   7798   7800   7806   7807   7811 
##      1      1      2      1      1      1      1      1      1      1 
##   7816   7817   7822   7823   7825   7846   7852   7856   7857   7862 
##      1      1      1      1      1      1      2      2      2      2 
##   7865   7867   7873   7879   7886   7887   7888   7890   7896   7898 
##      1      1      2      1      1      1      1      1      1      1 
##   7900   7901   7903   7906   7907   7911   7923   7926   7927   7933 
##      1      1      1      1      1      1      1      1      1      1 
##   7934   7936   7939   7940   7949   7950   7951   7952   7953   7956 
##      1      1      1      1      1      1      2      1      1      1 
##   7957   7962   7964   7967   7971   7972   7979   7983   7984   7985 
##      1      1      1      1      3      1      2      1      1      1 
##   7997   8000   8008   8010   8017   8020   8023   8024   8028   8029 
##      1      1      1      1      1      1      1      1      1      1 
##   8034   8036   8037   8038   8040   8044   8047   8051   8054   8061 
##      2      1      1      1      2      1      1      2      1      1 
##   8063   8066   8079   8083   8084   8091   8095   8102   8109   8110 
##      1      1      1      1      1      1      1      1      1      1 
##   8114   8120   8122   8128   8129   8134   8136   8137   8142   8146 
##      1      1      3      1      1      1      1      1      1      2 
##   8147   8148   8150   8162   8163   8166   8168   8169   8170   8173 
##      1      1      1      2      1      2      1      1      1      1 
##   8174   8176   8177   8181   8186   8211   8217   8219   8226   8237 
##      1      1      1      2      1      1      1      1      1      1 
##   8238   8243   8246   8252   8257   8262   8265   8272   8274   8278 
##      1      1      1      1      1      1      1      1      2      1 
##   8279   8282   8283   8287   8289   8292   8297   8301   8304   8313 
##      2      2      2      1      1      1      1      1      2      3 
##   8314   8325   8333   8334   8343   8344   8349   8352   8355   8358 
##      1      1      1      1      1      1      1      1      1      1 
##   8359   8364   8369   8384   8385   8388   8400   8411   8415   8422 
##      3      1      1      1      1      1      2      1      1      1 
##   8427   8428   8451   8452   8453   8461   8462   8463   8465   8466 
##      1      1      1      1      1      2      1      2      1      2 
##   8482   8487   8488   8492   8493   8495   8496   8513   8515   8536 
##      2      1      1      1      1      1      1      2      1      1 
##   8545   8546   8549   8552   8572   8576   8579   8586   8588   8589 
##      1      1      1      1      1      2      1      1      1      1 
##   8592   8593   8598   8601   8602   8603   8609   8619   8627   8637 
##      1      1      1      1      1      1      1      3      1      1 
##   8640   8645   8659   8660   8664   8665   8678   8679   8706   8716 
##      1      1      1      1      1      1      1      1      1      1 
##   8718   8721   8728   8731   8741   8743   8745   8746   8752   8753 
##      1      1      1      1      1      1      1      2      1      1 
##   8755   8761   8767   8768   8773   8776   8780   8782   8789   8793 
##      1      1      1      1      2      1      1      1      2      1 
##   8798   8799   8804   8813   8816   8820   8825   8828   8829   8844 
##      1      1      2      1      2      1      1      1      1      2 
##   8873   8877   8882   8886   8889   8897   8900   8908   8910   8912 
##      3      1      1      1      1      1      1      1      1      1 
##   8918   8921   8922   8923   8925   8926   8928   8929   8931   8935 
##      1      1      1      1      1      1      1      1      1      1 
##   8938   8947   8948   8950   8952   8957   8958   8959   8961   8978 
##      1      1      2      1      1      1      1      1      2      1 
##   8980   8983   8988   8997   9000   9008   9009   9012   9015   9018 
##      2      1      1      1      1      1      1      1      1      1 
##   9023   9039   9040   9043   9046   9047   9050   9055   9059   9063 
##      3      1      1      1      1      1      1      1      1      1 
##   9069   9081   9086   9087   9091   9093   9105   9110   9113   9116 
##      1      1      1      1      2      1      1      1      2      1 
##   9117   9122   9129   9136   9138   9152   9153   9156   9160   9163 
##      1      1      2      1      1      1      2      1      1      1 
##   9168   9172   9173   9180   9183   9185   9188   9195   9198   9201 
##      1      1      1      1      1      3      1      1      1      1 
##   9205   9213   9218   9219   9243   9254   9258   9267   9273   9285 
##      1      1      1      1      1      1      2      1      1      1 
##   9300   9319   9320   9321   9324   9342   9343   9348   9350   9353 
##      1      1      1      3      1      1      1      1      1      2 
##   9375   9379   9380   9384   9388   9401   9406   9422   9425   9431 
##      2      1      2      1      1      1      1      1      2      1 
##   9437   9440   9448   9453   9454   9457   9462   9466   9467   9482 
##      1      1      1      1      1      2      1      2      1      1 
##   9484   9493   9497   9510   9511   9516   9537   9545   9548   9549 
##      1      1      2      1      1      1      1      1      1      1 
##   9562   9567   9574   9580   9581   9585   9609   9614   9620   9637 
##      1      1      1      1      1      1      1      1      1      1 
##   9639   9642   9650   9657   9660   9662   9665   9666   9669   9670 
##      1      1      1      1      1      1      1      1      1      1 
##   9673   9674   9682   9687   9698   9699   9700   9702   9714   9715 
##      1      1      1      2      1      1      1      1      1      1 
##   9716   9728   9731   9737   9743   9746   9749   9750   9753   9755 
##      1      1      1      1      1      1      1      1      1      2 
##   9763   9771   9776   9778   9782   9785   9790   9795   9802   9807 
##      1      4      1      2      1      1      1      2      1      1 
##   9813   9814   9816   9825   9838   9848   9857   9860   9867   9868 
##      1      1      1      1      1      1      1      1      1      2 
##   9869   9879   9912   9927   9935   9937   9938   9941   9943   9951 
##      1      1      1      1      1      1      1      1      2      1 
##   9956   9959   9963   9964   9970   9974   9977   9979   9984   9987 
##      1      1      1      1      1      1      1      1      2      1 
##   9996   9998   9999  10006  10013  10026  10028  10037  10047  10054 
##      1      1      2      1      1      1      2      1      1      1 
##  10056  10068  10076  10078  10083  10084  10085  10096  10100  10108 
##      3      1      3      1      1      2      1      1      1      1 
##  10115  10134  10137  10146  10147  10149  10151  10153  10159  10167 
##      1      2      2      1      2      1      1      1      1      1 
##  10169  10176  10177  10178  10188  10193  10197  10198  10207  10221 
##      1      1      1      2      1      1      2      1      1      1 
##  10224  10232  10235  10238  10239  10240  10251  10253  10262  10274 
##      1      1      2      1      2      1      3      1      1      1 
##  10278  10280  10281  10284  10285  10293  10298  10299  10302  10304 
##      1      1      1      1      1      2      3      1      1      1 
##  10310  10314  10320  10322  10325  10333  10336  10338  10349  10352 
##      1      1      1      1      1      1      1      2      1      1 
##  10355  10357  10360  10361  10367  10377  10378  10383  10404  10405 
##      1      1      1      1      1      1      1      1      1      1 
##  10414  10418  10428  10433  10438  10445  10450  10455  10458  10467 
##      1      1      1      1      1      1      1      1      1      2 
##  10469  10478  10481  10485  10486  10488  10490  10502  10510  10525 
##      1      1      1      1      2      1      2      2      1      1 
##  10527  10528  10530  10538  10549  10551  10554  10555  10573  10574 
##      1      2      1      1      1      2      1      1      1      1 
##  10577  10584  10585  10597  10599  10602  10603  10605  10611  10612 
##      2      1      1      1      1      3      2      1      1      3 
##  10613  10626  10629  10632  10633  10636  10641  10643  10651  10654 
##      1      2      1      1      1      1      1      1      1      1 
##  10658  10663  10664  10665  10673  10681  10687  10690  10692  10696 
##      2      1      1      1      1      1      1      1      1      2 
##  10700  10705  10711  10716  10719  10720  10721  10727  10730  10747 
##      1      1      1      1      1      1      1      1      1      2 
##  10755  10758  10770  10774  10776  10783  10785  10794  10796  10797 
##      1      1      1      1      1      1      3      1      1      1 
##  10807  10810  10826  10829  10830  10837  10850  10854  10877  10879 
##      1      1      1      1      1      1      1      1      2      1 
##  10884  10892  10913  10926  10930  10937  10942  10944  10948  10961 
##      1      1      1      1      2      1      1      1      1      1 
##  10969  10970  10972  10978  10986  10991  10993  10995  11000  11002 
##      1      2      1      1      1      1      1      3      1      1 
##  11005  11014  11015  11032  11033  11035  11057  11058  11060  11081 
##      1      1      1      1      1      2      1      1      1      1 
##  11091  11092  11105  11108  11113  11126  11130  11133  11134  11135 
##      1      1      1      1      1      1      1      1      1      1 
##  11146  11156  11158  11174  11176  11184  11187  11189  11190  11199 
##      1      1      1      1      1      1      1      1      1      1 
##  11206  11225  11226  11227  11228  11230  11240  11250  11259  11264 
##      1      2      1      1      2      1      1      1      1      1 
##  11277  11278  11280  11287  11297  11300  11303  11316  11319  11320 
##      1      1      1      2      1      1      1      1      1      1 
##  11331  11341  11348  11350  11351  11369  11370  11374  11379  11383 
##      1      1      1      1      1      1      1      1      1      1 
##  11384  11392  11396  11407  11414  11416  11442  11446  11449  11453 
##      1      1      1      1      1      1      1      1      1      1 
##  11459  11480  11501  11502  11510  11512  11518  11520  11524  11527 
##      1      1      1      1      1      1      1      1      1      1 
##  11531  11532  11533  11538  11555  11556  11563  11574  11588  11590 
##      1      1      1      1      1      1      1      1      1      1 
##  11591  11595  11599  11600  11602  11615  11623  11627  11630  11631 
##      1      1      1      1      1      1      1      1      1      2 
##  11640  11645  11652  11661  11671  11678  11679  11682  11699  11700 
##      1      2      1      1      1      1      1      1      2      1 
##  11716  11721  11724  11725  11744  11746  11750  11755  11760  11766 
##      1      1      1      1      3      1      1      1      2      1 
##  11775  11788  11803  11808  11815  11816  11820  11830  11833  11834 
##      1      1      1      1      1      1      1      1      2      1 
##  11839  11858  11867  11882  11896  11898  11907  11914  11918  11926 
##      1      1      1      1      2      1      1      1      1      2 
##  11935  11938  11945  11948  11949  11952  11953  11960  11970  11976 
##      1      2      2      1      1      1      2      1      1      2 
##  11983  11986  11995  12001  12022  12023  12025  12036  12038  12054 
##      1      1      2      1      1      1      1      1      1      1 
##  12055  12058  12071  12077  12080  12082  12101  12104  12112  12113 
##      1      1      1      1      1      2      1      1      1      1 
##  12116  12127  12143  12145  12146  12147  12154  12157  12160  12164 
##      1      1      1      1      1      1      1      1      1      1 
##  12169  12170  12174  12195  12198  12200  12204  12216  12217  12218 
##      1      1      1      1      1      1      1      1      1      1 
##  12225  12226  12233  12237  12238  12241  12252  12262  12277  12278 
##      1      1      1      1      2      1      1      1      1      1 
##  12286  12287  12294  12295  12301  12304  12307  12320  12322  12324 
##      1      1      1      1      1      1      1      1      1      1 
##  12333  12334  12336  12345  12348  12353  12356  12361  12367  12375 
##      1      1      1      1      1      1      1      1      1      2 
##  12379  12382  12384  12386  12395  12403  12404  12417  12420  12426 
##      1      1      1      1      1      1      1      1      2      1 
##  12433  12439  12441  12455  12458  12462  12476  12478  12480  12501 
##      1      1      1      1      1      1      1      1      1      1 
##  12514  12533  12535  12550  12565  12571  12572  12588  12592  12594 
##      1      1      1      1      2      1      1      2      1      2 
##  12607  12608  12622  12638  12639  12642  12656  12668  12676  12684 
##      1      1      1      1      1      1      1      1      1      1 
##  12698  12705  12738  12740  12750  12751  12755  12756  12758  12774 
##      1      2      1      1      1      2      1      1      1      1 
##  12786  12791  12792  12795  12796  12799  12803  12806  12814  12820 
##      1      1      1      1      1      1      1      3      1      1 
##  12833  12834  12843  12849  12850  12851  12864  12881  12890  12898 
##      1      1      1      1      1      1      1      1      1      1 
##  12901  12911  12923  12928  12940  12947  12958  12977  12979  12989 
##      2      2      1      2      1      1      1      1      1      1 
##  12992  12999  13006  13008  13010  13014  13015  13022  13023  13026 
##      1      1      1      1      1      1      1      1      1      1 
##  13031  13036  13052  13053  13063  13067  13070  13072  13078  13084 
##      1      1      1      2      1      1      1      1      1      2 
##  13092  13095  13112  13121  13123  13124  13140  13148  13150  13155 
##      3      1      1      1      2      1      1      1      1      1 
##  13159  13165  13180  13185  13194  13196  13203  13213  13215  13235 
##      4      1      1      1      1      1      1      1      1      1 
##  13236  13239  13248  13252  13256  13258  13259  13271  13279  13280 
##      1      1      2      2      1      2      1      1      1      1 
##  13304  13311  13315  13317  13321  13325  13342  13343  13351  13352 
##      1      1      1      1      1      1      1      2      1      2 
##  13353  13355  13356  13363  13364  13365  13370  13391  13394  13413 
##      1      1      1      1      1      1      1      2      1      1 
##  13414  13432  13433  13452  13460  13466  13471  13487  13495  13498 
##      1      1      1      2      1      1      1      1      2      1 
##  13507  13509  13526  13543  13552  13555  13561  13572  13581  13588 
##      1      1      1      1      1      1      1      1      1      1 
##  13589  13604  13606  13611  13614  13618  13627  13639  13652  13653 
##      1      1      1      1      2      1      2      1      1      1 
##  13655  13672  13675  13680  13695  13721  13723  13727  13728  13733 
##      1      1      1      1      1      1      1      1      1      2 
##  13744  13777  13780  13783  13788  13794  13798  13801  13807  13808 
##      1      1      1      2      2      1      1      1      1      1 
##  13811  13817  13837  13880  13881  13889  13892  13895  13902  13904 
##      1      1      1      1      1      1      1      1      1      1 
##  13931  13934  13937  13939  13953  13967  13970  13972  13986  14010 
##      1      1      1      1      1      1      1      1      1      1 
##  14018  14028  14030  14034  14045  14046  14068  14085  14090  14094 
##      1      1      1      1      2      1      1      1      1      1 
##  14129  14153  14154  14155  14170  14186  14194  14201  14204  14205 
##      1      1      1      1      1      1      1      1      1      1 
##  14210  14211  14212  14222  14223  14228  14238  14239  14251  14256 
##      1      1      1      1      1      1      1      1      1      1 
##  14273  14274  14310  14319  14323  14324  14331  14333  14350  14352 
##      1      1      2      1      1      1      1      1      1      1 
##  14366  14379  14394  14409  14432  14437  14440  14446  14450  14457 
##      1      1      1      1      1      1      1      1      1      1 
##  14464  14485  14489  14500  14503  14504  14505  14515  14517  14519 
##      1      1      1      1      1      1      1      1      1      1 
##  14543  14546  14561  14577  14581  14620  14621  14639  14645  14646 
##      1      1      1      1      1      1      3      4      1      1 
##  14647  14660  14661  14664  14670  14672  14689  14692  14695  14700 
##      1      1      1      1      1      1      1      1      1      1 
##  14712  14729  14731  14738  14747  14750  14755  14760  14767  14771 
##      1      1      1      1      1      1      1      1      1      1 
##  14790  14795  14797  14799  14800  14815  14821  14850  14851  14855 
##      1      1      1      1      1      1      1      1      1      1 
##  14856  14868  14900  14904  14906  14908  14909  14910  14930  14935 
##      1      2      1      1      1      1      1      1      1      1 
##  14939  14941  14977  14981  14982  15019  15021  15023  15024  15027 
##      1      1      1      1      1      1      1      1      1      1 
##  15028  15037  15043  15061  15066  15068  15073  15091  15107  15143 
##      1      1      1      1      1      1      1      1      1      1 
##  15155  15159  15175  15184  15193  15205  15208  15241  15245  15250 
##      1      1      1      1      1      1      1      1      1      1 
##  15251  15270  15281  15302  15312  15330  15335  15336  15340  15356 
##      1      1      1      2      1      1      2      3      1      1 
##  15375  15382  15384  15392  15394  15398  15413  15448  15451  15457 
##      1      1      1      2      2      1      1      1      1      2 
##  15460  15467  15486  15488  15506  15507  15514  15526  15527  15539 
##      1      1      1      1      1      1      1      1      1      1 
##  15543  15547  15549  15564  15565  15567  15568  15571  15591  15598 
##      1      1      1      1      1      1      1      1      1      1 
##  15599  15604  15623  15628  15663  15684  15689  15698  15715  15730 
##      1      1      1      2      1      1      1      1      1      1 
##  15733  15741  15760  15772  15799  15820  15865  15867  15869  15875 
##      1      1      1      1      1      1      1      2      1      1 
##  15882  15883  15890  15896  15899  15906  15914  15920  15942  15954 
##      1      1      1      1      1      1      1      1      1      1 
##  15987  15995  16000  16004  16012  16017  16018  16020  16046  16049 
##      2      1      1      2      1      1      1      1      1      1 
##  16055  16056  16067  16077  16087  16095  16107  16128  16133  16136 
##      1      1      2      1      1      3      1      1      1      1 
##  16142  16159  16167  16181  16191  16201  16226  16255  16257  16302 
##      1      2      1      1      1      1      1      1      2      1 
##  16331  16347  16356  16363  16365  16389  16399  16400  16405  16412 
##      1      1      1      1      1      1      1      2      1      1 
##  16421  16443  16451  16452  16458  16460  16467  16494  16497  16525 
##      1      1      1      1      1      1      1      1      1      1 
##  16546  16547  16563  16567  16574  16584  16586  16592  16594  16610 
##      1      1      1      1      1      1      1      1      1      1 
##  16614  16668  16688  16748  16751  16757  16761  16792  16808  16813 
##      1      2      1      1      1      1      1      1      1      1 
##  16821  16826  16828  16836  16855  16866  16868  16882  16885  16933 
##      1      1      1      1      1      1      1      3      1      1 
##  16942  16953  16970  16975  17000  17002  17009  17012  17032  17042 
##      1      1      1      1      1      1      1      1      1      1 
##  17044  17051  17056  17070  17083  17084  17092  17097  17103  17117 
##      1      1      1      1      1      1      1      1      1      1 
##  17126  17133  17139  17148  17165  17167  17175  17186  17188  17191 
##      1      1      1      1      1      1      1      1      1      1 
##  17197  17201  17203  17209  17219  17234  17252  17261  17273  17290 
##      1      1      1      1      1      1      1      1      1      2 
##  17316  17354  17368  17377  17396  17404  17408  17420  17422  17430 
##      1      1      1      1      2      1      1      1      1      1 
##  17444  17459  17460  17462  17477  17489  17496  17529  17530  17533 
##      1      1      1      1      1      1      1      1      1      1 
##  17546  17547  17560  17588  17590  17591  17594  17597  17607  17643 
##      1      1      1      1      1      1      1      1      1      1 
##  17644  17649  17667  17689  17707  17715  17724  17727  17731  17741 
##      1      1      1      1      1      1      1      1      1      1 
##  17761  17774  17792  17829  17833  17860  17868  17871  17872  17891 
##      2      1      1      1      1      1      1      1      1      1 
##  17895  17909  17911  17920  17943  17984  17989  17998  18037  18067 
##      2      1      1      1      1      1      1      1      1      1 
##  18077  18079  18084  18093  18095  18103  18134  18136  18138  18156 
##      1      1      1      1      1      1      1      1      1      1 
##  18170  18201  18205  18210  18214  18226  18239  18254  18265  18274 
##      1      1      1      1      1      1      1      1      1      1 
##  18288  18302  18312  18319  18324  18325  18330  18340  18344  18352 
##      1      1      1      1      1      1      1      1      2      1 
##  18355  18359  18364  18375  18376  18377  18403  18406  18432  18447 
##      1      1      1      1      1      1      1      1      1      1 
##  18454  18458  18475  18480  18499  18509  18532  18534  18536  18537 
##      1      1      1      1      1      1      1      1      1      1 
##  18547  18576  18580  18581  18584  18628  18632  18652  18667  18671 
##      1      1      1      1      1      3      1      1      1      1 
##  18674  18678  18686  18698  18718  18720  18723  18729  18737  18747 
##      5      2      1      1      1      1      1      1      1      1 
##  18822  18839  18854  18859  18861  18866  18893  18908  18929  18930 
##      1      1      1      1      1      1      1      1      1      2 
##  18932  18971  18978  18983  18986  18992  18998  19014  19018  19038 
##      1      1      2      1      1      1      1      1      1      1 
##  19053  19063  19090  19100  19104  19108  19135  19145  19156  19163 
##      1      1      1      1      1      1      1      1      1      1 
##  19165  19172  19193  19212  19226  19260  19263  19268  19277  19302 
##      1      1      2      1      1      3      1      1      1      2 
##  19315  19321  19328  19341  19349  19369  19401  19403  19435  19453 
##      1      2      1      1      1      1      1      1      1      1 
##  19458  19460  19474  19498  19501  19541  19584  19589  19608  19612 
##      1      1      1      1      1      1      1      1      1      1 
##  19638  19641  19659  19664  19681  19685  19688  19690  19695  19704 
##      1      1      1      2      1      1      1      1      1      1 
##  19707  19710  19722  19725  19726  19738  19754  19756  19772  19773 
##      1      1      2      1      1      1      1      1      1      1 
##  19779  19796  19849  19861  19869  19890  19911  19923  19963  20012 
##      1      1      1      1      1      1      1      1      1      1 
##  20058  20067  20095  20100  20107  20112  20118  20128  20135  20149 
##      1      1      1      1      1      1      1      1      1      1 
##  20150  20164  20172  20185  20207  20210  20218  20235  20241  20285 
##      1      1      1      1      1      1      1      1      1      1 
##  20286  20328  20348  20349  20373  20469  20472  20503  20510  20533 
##      1      1      1      1      1      1      1      1      1      2 
##  20542  20589  20604  20641  20647  20657  20664  20674  20681  20700 
##      1      1      1      1      2      1      1      1      1      1 
##  20729  20730  20763  20779  20785  20811  20851  20869  20874  20886 
##      1      1      1      1      1      1      1      1      1      1 
##  20907  20911  20928  20944  20965  20979  20990  21009  21018  21019 
##      1      1      1      1      1      1      2      1      1      1 
##  21026  21042  21060  21126  21135  21139  21147  21149  21157  21166 
##      1      1      1      1      3      1      1      1      3      1 
##  21195  21216  21251  21266  21276  21285  21297  21299  21323  21350 
##      1      1      1      1      1      1      1      1      1      1 
##  21369  21393  21400  21404  21446  21460  21465  21500  21505  21541 
##      1      2      1      1      1      1      1      1      1      1 
##  21567  21615  21618  21628  21636  21659  21691  21723  21751  21758 
##      1      1      1      1      1      1      1      1      1      1 
##  21783  21844  21858  21891  21893  21904  21905  21909  21928  21944 
##      1      1      1      1      1      1      1      1      1      1 
##  21969  21972  21980  21989  22010  22049  22058  22091  22093  22115 
##      1      1      1      1      1      1      1      1      1      1 
##  22144  22155  22165  22169  22174  22177  22187  22221  22228  22245 
##      1      1      1      1      1      1      1      1      1      1 
##  22264  22271  22273  22284  22291  22307  22332  22397  22431  22435 
##      1      1      1      2      1      1      1      1      1      1 
##  22449  22495  22502  22526  22529  22555  22578  22624  22668  22674 
##      1      1      1      1      1      1      1      1      1      1 
##  22682  22697  22713  22754  22757  22775  22776  22793  22831  22855 
##      1      2      1      1      1      1      1      1      1      2 
##  22871  22882  22889  22903  22922  22925  22929  22947  22963  22969 
##      1      1      1      1      1      1      1      1      1      1 
##  22994  23029  23034  23044  23057  23064  23066  23096  23100  23102 
##      1      1      1      2      1      1      1      4      3      1 
##  23107  23109  23129  23189  23210  23251  23254  23262  23302  23308 
##      1      1      1      1      1      1      1      1      1      1 
##  23320  23368  23415  23423  23472  23473  23476  23505  23511  23535 
##      1      1      1      1      1      1      1      1      2      1 
##  23549  23552  23562  23571  23601  23610  23626  23630  23644  23650 
##      1      1      1      1      1      1      3      1      1      1 
##  23660  23668  23671  23676  23727  23740  23748  23752  23754  23756 
##      2      1      1      1      1      1      1      1      1      2 
##  23759  23772  23802  23835  23867  23880  23931  23960  23973  23983 
##      1      1      1      1      1      1      1      1      1      1 
##  23984  24008  24012  24024  24026  24046  24050  24070  24072  24089 
##      1      1      1      1      1      1      1      1      1      1 
##  24096  24099  24115  24132  24150  24173  24177  24184  24199  24237 
##      1      1      2      1      1      1      1      1      1      1 
##  24251  24270  24280  24291  24297  24350  24351  24364  24400  24413 
##      1      2      1      1      1      1      2      1      1      1 
##  24442  24444  24476  24512  24589  24592  24614  24632  24642  24665 
##      1      1      2      1      1      1      1      1      1      1 
##  24675  24677  24701  24762  24763  24802  24808  24831  24850  24858 
##      1      1      1      1      1      2      1      1      1      1 
##  24865  24871  24910  24940  24975  24981  24998  25000  25018  25045 
##      1      1      1      1      1      1      1      1      1      1 
##  25054  25067  25108  25119  25133  25153  25166  25170  25218  25224 
##      1      1      1      1      1      1      1      1      1      1 
##  25255  25257  25270  25274  25280  25307  25320  25360  25389  25392 
##      1      1      1      1      1      1      1      1      2      1 
##  25464  25476  25500  25512  25579  25589  25611  25623  25627  25645 
##      1      1      1      1      1      1      1      1      1      1 
##  25651  25662  25664  25730  25735  25766  25781  25784  25911  25928 
##      1      1      1      1      1      2      1      1      1      1 
##  25980  26017  26043  26057  26070  26085  26098  26107  26124  26172 
##      1      1      1      1      1      1      1      1      1      1 
##  26175  26231  26331  26403  26412  26436  26450  26487  26536  26593 
##      2      1      1      1      1      1      1      1      1      1 
##  26600  26601  26622  26623  26673  26679  26704  26752  26795  26811 
##      1      1      1      1      2      1      1      1      1      1 
##  26813  26815  26818  26836  26838  26843  26931  26955  26978  26987 
##      1      1      1      1      1      1      1      1      1      1 
##  26989  27011  27021  27031  27060  27065  27075  27090  27098  27106 
##      1      1      1      1      1      1      1      1      1      1 
##  27129  27136  27150  27198  27311  27367  27400  27404  27460  27466 
##      2      1      1      1      1      1      1      1      1      2 
##  27491  27528  27551  27558  27649  27651  27663  27719  27755  27784 
##      1      1      1      1      1      1      1      1      1      1 
##  27787  27870  27883  27898  27927  27969  27997  28014  28034  28057 
##      1      1      1      1      1      1      1      1      1      1 
##  28065  28070  28094  28114  28125  28133  28147  28172  28174  28175 
##      1      1      1      1      1      1      1      1      1      1 
##  28200  28247  28255  28260  28277  28389  28410  28433  28463  28464 
##      1      2      1      1      1      1      1      1      1      1 
##  28473  28502  28504  28505  28587  28591  28600  28649  28667  28681 
##      1      1      1      1      1      2      1      1      1      1 
##  28684  28740  28782  28840  28929  28963  29072  29074  29082  29119 
##      1      1      1      1      1      1      2      1      1      1 
##  29140  29156  29183  29207  29246  29285  29319  29335  29369  29375 
##      1      1      1      1      1      1      1      1      1      1 
##  29403  29429  29446  29448  29487  29489  29537  29687  29688  29719 
##      1      1      1      1      1      1      1      1      1      1 
##  29776  29795  29809  29875  29876  29882  29997  30023  30027  30097 
##      1      2      1      1      1      1      1      1      1      1 
##  30112  30119  30202  30231  30239  30347  30402  30408  30417  30441 
##      1      1      1      1      1      1      1      1      1      1 
##  30453  30500  30520  30563  30579  30588  30645  30664  30667  30682 
##      1      1      1      1      1      1      1      1      1      1 
##  30691  30747  30777  30803  30920  30928  30948  30970  30997  30998 
##      1      1      1      1      1      1      1      1      1      1 
##  31013  31031  31035  31041  31099  31115  31176  31251  31297  31348 
##      1      1      1      1      1      1      1      1      1      1 
##  31352  31392  31404  31497  31533  31541  31550  31605  31622  31631 
##      1      1      1      1      1      1      1      1      1      1 
##  31761  31847  31894  31913  31919  32005  32006  32069  32110  32119 
##      1      1      1      1      1      1      1      1      1      1 
##  32138  32175  32200  32254  32326  32390  32396  32413  32497  32500 
##      1      1      1      1      1      1      1      1      1      1 
##  32576  32645  32683  32698  32755  32766  32790  32859  32946  32961 
##      1      1      1      1      1      1      1      1      1      1 
##  32969  33036  33057  33134  33135  33154  33240  33323  33324  33337 
##      3      1      1      1      1      2      1      1      1      1 
##  33376  33432  33463  33506  33509  33520  33555  33566  33628  33646 
##      1      1      1      1      1      1      1      1      1      1 
##  33773  33783  33801  33803  33835  33852  33863  33888  33925  33929 
##      1      1      1      1      1      1      1      1      1      1 
##  33998  34133  34171  34183  34193  34225  34336  34381  34388  34416 
##      1      1      1      1      1      1      1      1      1      1 
##  34434  34435  34525  34555  34645  34666  34794  34836  34874  34876 
##      1      1      1      1      1      1      1      1      2      1 
##  34880  34899  34911  34968  34977  34988  34990  34997  35008  35055 
##      1      2      1      1      1      1      1      1      1      1 
##  35096  35097  35119  35128  35169  35185  35212  35227  35250  35299 
##      1      1      1      1      1      1      1      1      1      1 
##  35334  35374  35454  35457  35459  35471  35514  35574  35727  35794 
##      1      1      1      1      1      1      1      1      3      1 
##  35849  35901  35927  35972  36153  36302  36363  36384  36471  36477 
##      2      1      1      1      1      1      1      1      1      1 
##  36492  36514  36598  36626  36863  36961  37003  37077  37212  37287 
##      1      1      1      1      1      1      1      1      1      1 
##  37291  37316  37317  37329  37339  37454  37463  37534  37642  37643 
##      1      1      1      1      1      2      1      1      1      1 
##  37655  37837  37855  37919  37936  37998  38068  38108  38149  38160 
##      1      1      1      1      1      1      1      1      1      1 
##  38212  38286  38304  38336  38365  38417  38432  38475  38489  38657 
##      1      1      1      1      1      1      1      1      1      1 
##  38660  38664  38665  38709  38870  38960  38996  39011  39028  39210 
##      3      1      1      1      1      1      1      1      1      1 
##  39227  39295  39379  39409  39470  39473  39484  39632  39856  39986 
##      1      1      1      1      1      1      1      1      1      1 
##  40013  40087  40189  40335  40389  40392  40482  40485  40527  40553 
##      1      2      1      1      1      1      1      1      1      1 
##  40633  40779  40836  40938  41014  41020  41214  41244  41361  41374 
##      1      2      1      1      1      4      1      1      1      1 
##  41378  41386  41661  41694  41763  41822  41975  42205  42342  42370 
##      1      1      1      1      1      1      1      1      1      1 
##  42387  42485  42488  42556  42824  42854  42881  42962  43064  43079 
##      1      1      1      1      1      1      1      1      1      1 
##  43093  43121  43200  43322  43363  43367  43437  43607  43642  43722 
##      1      1      1      1      1      1      1      1      1      1 
##  43761  43776  43789  43958  44036  44203  44262  44307  44369  44493 
##      1      1      1      1      1      1      1      1      1      1 
##  44734  44744  44859  44879  45059  45201  45202  45298  45364  45655 
##      1      1      1      1      1      1      1      1      1      1 
##  45726  45857  45864  45979  46010  46065  46099  46127  46216  46255 
##      1      1      1      1      1      1      1      1      2      1 
##  46331  46359  46394  46642  46943  46989  47008  47371  47625  47746 
##      1      1      1      1      1      1      1      1      1      1 
##  47766  47918  47963  47965  48009  48024  48100  48121  48150  48201 
##      1      1      1      1      1      1      1      1      2      1 
##  48289  48423  48487  48673  48703  48865  48992  49047  49116  49178 
##      1      1      1      2      1      1      1      1      1      1 
##  49229  49248  49274  49283  49454  49466  49759  49809  49818  49868 
##      1      1      1      1      1      1      1      1      1      1 
##  49924  50017  50163  50261  50385  50396  50421  50610  50688  50852 
##      1      1      1      1      1      1      1      1      1      1 
##  51103  51119  51252  51344  51370  51788  51847  52033  52047  52379 
##      1      1      1      1      1      1      1      1      1      1 
##  52456  52480  52612  52820  52844  53054  53083  53148  53215  53335 
##      1      1      1      1      1      1      1      1      1      1 
##  53351  53420  53439  53442  53622  53798  53824  54000  54007  54068 
##      1      1      1      1      1      1      1      1      1      1 
##  54364  54480  54550  54596  54782  54881  54915  54918  55111  55462 
##      1      1      1      1      1      1      1      1      1      1 
##  55716  55869  55958  56254  56288  56502  56716  56743  57252  57265 
##      1      1      1      1      1      1      1      1      1      1 
##  57376  57580  57884  57979  58221  58365  58463  58521  58565  58583 
##      1      1      1      1      1      1      1      1      1      1 
##  58678  58708  58858  59241  59415  59613  59692  59860  59883  60170 
##      1      1      1      1      1      1      2      1      1      1 
##  60308  60310  60346  60433  60510  60571  60616  60966  60997  61085 
##      1      1      1      1      1      1      1      1      1      1 
##  61231  61350  61393  61442  61564  61635  61745  61821  61981  62092 
##      1      1      1      1      1      1      1      1      1      1 
##  62129  62259  62312  62348  62512  62891  62903  63047  63217  63290 
##      1      1      1      1      1      1      1      1      1      1 
##  63373  63482  63558  63743  63897  64116  64420  64519  64538  64587 
##      1      1      1      2      1      1      1      1      1      1 
##  64595  64839  64868  65216  65320  65938  65951  65959  66422  66466 
##      1      1      1      1      1      1      1      1      1      1 
##  66600  66852  67434  67449  68013  68123  68304  68587  68828  68900 
##      1      1      1      1      1      2      1      1      1      1 
##  69276  69313  69483  69551  69823  69875  69907  70000  70132  70146 
##      1      1      1      1      1      1      1      1      1      1 
##  70334  70456  70567  70659  70734  70983  71328  72051  72112  72113 
##      1      1      1      5      1      1      1      1      1      1 
##  72121  72156  72302  72313  72705  72817  72997  73118  73323  73490 
##      1      1      1      1      1      1      1      1      1      1 
##  73661  73936  74579  74844  74990  75492  76008  76588  76840  77300 
##      1      2      2      1      1      1      1      1      1      1 
##  77384  77422  77771  77853  77985  78097  78380  78750  78935  79522 
##      1      1      1      1      1      1      1      1      1      1 
##  79574  80097  80346  80441  80646  80792  80975  81004  81495  81723 
##      1      1      1      1      1      1      1      1      1      1 
##  82271  82580  82708  82980  83138  83534  83756  83956  84427  84691 
##      1      1      1      1      1      1      1      1      1      1 
##  84834  84933  85065  85803  85885  85953  86101  86127  86282  86303 
##      1      1      1      1      1      1      1      1      1      1 
##  86351  86566  86730  87588  89000  89265  89523  89827  90536  90588 
##      2      1      1      1      1      1      1      1      1      1 
##  90756  91162  91501  91554  91636  91687  92177  92467  92753  93237 
##      1      1      1      1      1      1      2      1      1      1 
##  93593  95043  95280  95320  95389  95441  97020  97773  99792  99979 
##      1      1      1      1      1      1      1      1      1      1 
##  99991 101212 101497 101512 101644 102546 102936 102959 103076 103505 
##      2      1      1      1      1      1      1      2      1      1 
## 103709 103884 103975 104768 105340 105575 106071 106156 107319 107354 
##      1      1      1      1      1      1      2      1      1      1 
## 108415 109820 109956 110541 111524 111690 111873 112221 112684 113205 
##      1      1      1      1      1      1      1      1      1      1 
## 113552 114385 114872 116014 116896 117937 119147 119660 120153 120642 
##      1      1      1      1      1      1      1      1      1      1 
## 121379 122690 122868 123828 123871 124318 124471 124651 124691 124858 
##      1      1      1      1      1      1      1      2      1      1 
## 124888 126638 126830 127058 127472 127850 128639 128864 128993 129746 
##      1      1      1      1      1      1      2      1      1      1 
## 130093 131214 134322 135229 136476 142263 143329 144886 145618 149901 
##      1      1      1      3      1      1      1      1      2      1 
## 153237 155578 157422 158486 160039 161344 161475 161782 164607 165097 
##      1      1      1      1      1      1      1      1      1      1 
## 168648 171093 172240 173334 174862 175281 176347 179158 183396 188818 
##      1      1      1      1      1      1      1      1      1      1 
## 190585 192016 202741 205400 215315 223738 225595 230291 241707 242333 
##      1      1      1      1      1      1      1      1      1      1 
## 249209 255963 265084 279970 284169 327677 444745 463881 
##      1      1      1      1      1      1      1      1
ggplot(data = DelinquenciesValues, aes(x = AmountDelinquent))+
  geom_histogram(binwidth = 10)+
  coord_cartesian(xlim = c(0,2000))+
  ggtitle('Count of Loans by Amount Delinquent')

The data above in the histograms and table shows that the majority of Prosper borrowers have 0 dollars in delinquency, a good sign if you are a lender. After adjusting the histogram to account for this reality (removing all values with 0), we see that Prosper, as expected,

Borrower Data Exploration: Subsection: Delinquencies Last 7 Years

Examining the Delinquencies Last 7 Years variable will help us understand the type of borrowers that are included in this dataset. DelinquenciesLast7Years may provide a glimpse into the reliability of borrowers in this set.

sort(table(loans$DelinquenciesLast7Years), decreasing = T)
## 
##     0     1     3     2     4     5     6     7     8     9    10    11 
## 76439  3967  3183  2879  2592  1826  1790  1648  1421  1208  1151  1075 
##    12    13    14    15    16    17    18    20    19    21    23    24 
##   982   873   821   795   731   608   574   565   540   472   439   423 
##    22    25    26    27    28    29    30    32    31    35    33    34 
##   421   347   330   317   296   287   248   225   214   201   190   190 
##    37    39    36    38    42    40    44    99    41    43    47    46 
##   153   148   147   144   128   113   110   110   106   101    94    90 
##    45    48    49    50    51    52    56    60    53    54    55    62 
##    81    78    74    72    72    55    53    41    40    40    39    36 
##    59    61    65    58    63    57    64    66    67    75    68    69 
##    34    34    34    31    31    30    28    27    22    22    20    20 
##    73    70    77    72    71    80    82    76    78    74    88    79 
##    17    15    15    14    13    12    12    10    10     9     9     8 
##    84    86    87    90    83    92    89    81    91    95    96    97 
##     8     7     7     7     6     6     5     4     4     4     4     4 
##    85    94    98    93 
##     3     3     3     2
summary(loans$DelinquenciesLast7Years)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.000   0.000   4.155   3.000  99.000     990

Findings : Unsurprisingly, we see the vast majority of delinquent loans in the last 7 years for borrowers at 0. The median reflects this by also being 0, however, a mean of 4.155 shows that there are some potentially large amounts of delinquencies in the last 7 years per borrowers that may be driving this value up. In the table, we see that there are, in fact, 110 borrowers who have 99 delinquencies in the past 7 years. This appears to be a strange lift from 98 (3 total borrowers). Is this a maximum value? Could it be human error?

qplot(data = loans ,x=DelinquenciesLast7Years, binwidth = 1)+
  geom_histogram()+
  scale_x_continuous()+
  scale_y_continuous(
    limits = c(0,100000)
  )+
  ggtitle('Count of Delinquencies Last 7 Years')
## Warning: Removed 990 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 990 rows containing non-finite values (stat_bin).

Findings: A simple histogram shows that, in fact, the majority of delinquencies in last 7 years for borrowers were negatively skewed, unsurprisingly considering that banks and lenders are in the business of ensuring their loans are paid back. Let’s examine and plot that surreptitious the DelinquenciesLast7Years on the larger end of the plot.

qplot(data = loans, x = loans$DelinquenciesLast7Years)+
  geom_histogram(binwidth = 1)+
  scale_x_continuous(
    limits = c(80,100)
  )+
  ggtitle('Count of Delinquencies Last 7 years')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 113717 rows containing non-finite values (stat_bin).

## Warning: Removed 113717 rows containing non-finite values (stat_bin).

> Findings The histogram from DelinquenciesLast7Years > 79 show that the #99 is a strange occurance that may be artifically driving the mean up for the total DelinquenciesLast7Years. We will attempt to determine, later in this analysis, what makes an individual become delinquent with some multivariate tests and plots.

Borrower Data Exploration: Subsection: BorrowerAPR We are getting a better sense of the types of borrowers Prosper loans money to. Now, we will examine the BorrowerAPR to determine how Prosper makes $ of their customers.

qplot(data = loans ,x=BorrowerAPR)+
  geom_histogram(binwidth = .01)+
  ggtitle('Count of Loans by Borrower APR')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 25 rows containing non-finite values (stat_bin).

## Warning: Removed 25 rows containing non-finite values (stat_bin).

The findings above dictate a few peaks: Once between .15 and .20, again at .3, and once more at around .36. Let’s create a sorted table to examine these trends.

head(sort(table(loans$BorrowerAPR), decreasing = T), 20)
## 
## 0.35797 0.35643 0.37453 0.30532  0.2951 0.35356 0.29776 0.15833 0.24246 
##    3672    1644    1260     902     747     721     707     652     605 
## 0.24758 0.12528 0.17359 0.15324 0.27462 0.27285 0.13799 0.15713 0.12691 
##     601     559     549     547     534     506     489     482     456 
## 0.25781 0.20735 
##     444     433
summary(loans$BorrowerAPR)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## 0.00653 0.15629 0.20976 0.21883 0.28381 0.51229      25

Interestingly, we see that Prosper’s most commonly issued APR is .3672, this is well above the mean of .21976 and the median of .20976.

Let’s remove all NA’s from APR for analysis - adding the Mean line, we can examine how many values are falling above or below the mean.

Clean_APR <- subset(loans, !is.na(BorrowerAPR))
mean(Clean_APR$BorrowerAPR)
## [1] 0.2188277
qplot(data = Clean_APR ,x=BorrowerAPR, binwidth = .01)+
  geom_histogram()+
  scale_x_continuous(breaks = seq(0,0.4,.02))+
  geom_vline(xintercept = mean(Clean_APR$BorrowerAPR), color = 'green', linetype = 'longdash')+
  ggtitle('Count of Loans by Borrower APR')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

We see a number of peaks and valleys within the BorrowerAPR data, which suggests there are certain integers that Prosper commonly issues when it comes to BorrowerAPR.

Borrower Data Exploration: Subsection: Income Range

summary(loans$IncomeRange)
##             $0      $1-24,999      $100,000+ $25,000-49,999 $50,000-74,999 
##            621           7274          17337          32192          31050 
## $75,000-99,999  Not displayed   Not employed 
##          16916           7741            806
loans_IncomeRanges <- subset(loans, loans$IncomeRange != "Not displayed")
summary(loans_IncomeRanges$IncomeRange)
##             $0      $1-24,999      $100,000+ $25,000-49,999 $50,000-74,999 
##            621           7274          17337          32192          31050 
## $75,000-99,999  Not displayed   Not employed 
##          16916              0            806
qplot(data=loans_IncomeRanges, x=loans_IncomeRanges$IncomeRange)+
  geom_bar()+
  ggtitle('Count of Loans by Income Range')

Findings

qplot(data=loans, x=BorrowerState)+
  geom_bar()+
  ggtitle('Count of Loans by Borrower State')

sort(table(loans$BorrowerState), decreasing = T)
## 
##    CA    TX    NY    FL    IL          GA    OH    MI    VA    NJ    NC 
## 14717  6842  6729  6720  5921  5515  5008  4197  3593  3278  3097  3084 
##    WA    PA    MD    MO    MN    MA    CO    IN    AZ    WI    OR    TN 
##  3048  2972  2821  2615  2318  2242  2210  2078  1901  1842  1817  1737 
##    AL    CT    SC    NV    KS    KY    OK    LA    UT    AR    MS    NE 
##  1679  1627  1122  1090  1062   983   971   954   877   855   787   674 
##    ID    NH    NM    RI    HI    WV    DC    MT    DE    VT    AK    SD 
##   599   551   472   435   409   391   382   330   300   207   200   189 
##    IA    WY    ME    ND 
##   186   150   101    52

California has the largeset amount of users on Prosper with 14,717 borrowers, while North Dakota has the least with 52 borrowers.

Borrower Subsection: TotalInquiries

qplot(data=loans, x=TotalInquiries)+
  geom_histogram()+
  ggtitle('Count of Loans by Total Inquiries')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 1159 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 1159 rows containing non-finite values (stat_bin).

head(sort(table(loans$TotalInquiries), decreasing = T), 20)
## 
##     2     3     1     4     5     0     6     7     8     9    10    11 
## 14887 13934 13785 12148 10098  8430  7607  6171  4692  3779  2914  2431 
##    12    13    14    15    16    17    18    19 
##  1786  1453  1245   978   864   724   581   539

The data above show that most borrowers have very few inquiries on their credit, potentially showing that Prosper selects those who are steadfast and committed to paying down their debts.

qplot(data=loans, x=DebtToIncomeRatio)+
  geom_histogram()+
  ggtitle('Count of Loans by Debt To Income Ratio')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 8554 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 8554 rows containing non-finite values (stat_bin).

Given that the 10 value appears to be an anomaly, let’s run a summary on Debt to Income Ratio

summary(loans$DebtToIncomeRatio)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.140   0.220   0.276   0.320  10.010    8554

Let’s further examine Debt to Income Ratios that are above the 3rd Quartile

High_DTIR <- subset(loans, loans$DebtToIncomeRatio > .32)
sort(table(High_DTIR$DebtToIncomeRatio),decreasing = T)
## 
##    0.33    0.35    0.34    0.36    0.37    0.38    0.39     0.4    0.41 
##    1902    1812    1810    1523    1399    1364    1226    1109     995 
##    0.42    0.43    0.44    0.45    0.46    0.47    0.48    0.49     0.5 
##     893     851     753     697     634     617     524     470     447 
##    0.51    0.52    0.54    0.53    0.55   10.01    0.56    0.57    0.59 
##     431     372     341     320     279     272     244     229     182 
##    0.58     0.6    0.61    0.62    0.63    0.65    0.64    0.66    0.67 
##     166     149     140     120     108     105      91      78      77 
##    0.68    0.71     0.7    0.69    0.72    0.75    0.73    0.76    0.74 
##      72      67      64      58      58      51      43      43      40 
##    0.78    0.77    0.86    0.87    0.81    0.84    0.85    0.79    0.83 
##      38      35      29      29      27      27      27      26      26 
##     0.8    0.82    0.88    0.89     0.9    0.91    0.94    0.96    0.97 
##      24      22      22      22      20      19      19      19      18 
##    0.92    0.93       1    0.98    0.99    1.02    0.95    1.01    1.05 
##      15      14      14      13      13      12      11      11      11 
##    1.06    1.07    1.03    1.19    1.21    1.04    1.12    1.16    1.08 
##      11      11      10      10      10       8       8       8       7 
##     1.1    1.27    1.14    1.15    1.18    1.22    1.49     1.2    1.25 
##       7       7       6       6       6       6       6       5       5 
##    1.31    1.56    1.09    1.11    1.24    1.32    1.36    1.47    1.54 
##       5       5       4       4       4       4       4       4       4 
##     2.2    1.13    1.29    1.34    1.39    1.41    1.42    1.45    1.46 
##       4       3       3       3       3       3       3       3       3 
##     1.6    1.75    1.79    1.81    1.87    1.89    1.99     2.3    2.38 
##       3       3       3       3       3       3       3       3       3 
##    2.45    2.72    3.49    3.92    1.17    1.23    1.26    1.28     1.3 
##       3       3       3       3       2       2       2       2       2 
##    1.37    1.38     1.5    1.51    1.52    1.55    1.57    1.58    1.61 
##       2       2       2       2       2       2       2       2       2 
##    1.65    1.72    1.74     1.8    1.82    1.93    1.94    1.98    2.02 
##       2       2       2       2       2       2       2       2       2 
##    2.07     2.1    2.19    2.34     2.5     2.6    2.65    2.79    2.95 
##       2       2       2       2       2       2       2       2       2 
##    2.99    3.23    3.27    3.53    3.64    3.73    3.81     4.4    4.43 
##       2       2       2       2       2       2       2       2       2 
##    4.71     4.9    5.36    5.56    7.27 0.32007   0.321 0.32388 0.33348 
##       2       2       2       2       2       1       1       1       1 
## 0.34443 0.34452 0.35155 0.35333  0.3543  0.3555 0.35972 0.36006 0.36232 
##       1       1       1       1       1       1       1       1       1 
## 0.36331 0.37002 0.37772 0.38361  0.3838 0.38587 0.39181 0.39531 0.39846 
##       1       1       1       1       1       1       1       1       1 
## 0.40466 0.40475 0.40572  0.4137 0.41586 0.42965 0.42972 0.43886  0.4413 
##       1       1       1       1       1       1       1       1       1 
## 0.46403   0.499 0.50136 0.50872 0.51504 0.54433 0.56576 0.57091 0.60618 
##       1       1       1       1       1       1       1       1       1 
## 0.78342    1.35     1.4    1.43    1.44    1.53    1.59    1.62    1.64 
##       1       1       1       1       1       1       1       1       1 
##    1.66    1.67    1.68    1.69     1.7    1.73    1.76    1.78    1.85 
##       1       1       1       1       1       1       1       1       1 
##    1.86     1.9    1.92    1.95    1.96    2.05    2.08    2.09    2.11 
##       1       1       1       1       1       1       1       1       1 
##    2.14    2.16    2.18    2.21    2.22    2.23    2.25 2.27329    2.28 
##       1       1       1       1       1       1       1       1       1 
##    2.31    2.35    2.43    2.47    2.48    2.49    2.53    2.55    2.57 
##       1       1       1       1       1       1       1       1       1 
##    2.59    2.63    2.66    2.67     2.7    2.74    2.83    2.86    2.94 
##       1       1       1       1       1       1       1       1       1 
##    2.97    3.07    3.09    3.11    3.14    3.17    3.19    3.22    3.26 
##       1       1       1       1       1       1       1       1       1 
##    3.28    3.29    3.32    3.38    3.39    3.45    3.54    3.58    3.59 
##       1       1       1       1       1       1       1       1       1 
##    3.66    3.68    3.71    3.76    3.77    3.86       4    4.03    4.04 
##       1       1       1       1       1       1       1       1       1 
##    4.13    4.14    4.15    4.16    4.19    4.21    4.27    4.29    4.32 
##       1       1       1       1       1       1       1       1       1 
##    4.33    4.37    4.42    4.44    4.54    4.58    4.66    4.68    4.75 
##       1       1       1       1       1       1       1       1       1 
##    4.76    4.78    4.84    4.85    4.86    4.89    5.02    5.05    5.06 
##       1       1       1       1       1       1       1       1       1 
##     5.1    5.15    5.16    5.18    5.21    5.23    5.26    5.29    5.31 
##       1       1       1       1       1       1       1       1       1 
##    5.34    5.38    5.55  5.5608    5.59    5.64    5.65    5.67    5.69 
##       1       1       1       1       1       1       1       1       1 
##    5.76    5.98    6.01    6.05    6.06    6.07     6.2    6.37    6.49 
##       1       1       1       1       1       1       1       1       1 
##    6.51    6.66    6.68    6.85    6.95    6.96    7.06    7.22    7.42 
##       1       1       1       1       1       1       1       1       1 
##    7.47    7.52    7.59    7.79     7.9    7.99    8.06    8.13    8.27 
##       1       1       1       1       1       1       1       1       1 
##    8.52    8.53    8.63    9.06     9.2    9.44    9.77 
##       1       1       1       1       1       1       1

From the data above, that there are a few loans at various price points that have obscenely high debt to income ratios. Perhaps these folks have a great deal of collateral to put up.

qplot(data=loans, x=EmploymentStatus)+
  geom_bar()+
  ggtitle('Count of Loans by Employment Status')

The graph above shows that most borrowers are “employed” or categorized as “full-time”

qplot(data = loans, x=ProsperRating..numeric.)+
  geom_bar()+
  ggtitle('Count of Loans by Prosper Rating Numeric')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 29084 rows containing non-finite values (stat_bin).
## Warning: Removed 29084 rows containing non-finite values (stat_count).

Let’s examine the credit scores of applicant’s by creating a new variable that takes the mean of credit score upper and credit score lower. We will, when creating a histogram, start the x-axis at 300 to avoid lower values that are outliers or have omitted values.

loans$AvgCreditScore <- (loans$CreditScoreRangeLower + loans$CreditScoreRangeUpper) / 2
ggplot(data = loans, aes(x = loans$AvgCreditScore), binwidth = 50)+
  geom_histogram()+
  scale_x_continuous(breaks = seq(250,850,50), limits = c(250,850))+
  ggtitle('Count of Loans by Average Credit Score')
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 963 rows containing non-finite values (stat_bin).
## Warning: Removed 1 rows containing missing values (geom_bar).

From the above, we can see that most credit scores fall within 650 and 700. Let’s bucket those credit scores to create a categorical variable for later analysis.

loans$csBucket <- cut(loans$AvgCreditScore, breaks = c(400, 500, 600, 700, 800, 900))
ggplot(data = subset(loans, !is.na(csBucket)), aes(x=csBucket))+
  geom_bar()+
  ggtitle('Count of Loans by Credit Score Bucket')

When we look at the bucket bar chart below, we see there are a nearly equal amount of loans provided to average credit scores of between 600-700 and 700-800, with very few happening below or above.

Univariate Analysis

Tip: Now that you’ve completed your univariate explorations, it’s time to reflect on and summarize what you’ve found. Use the questions below to help you gather your observations and add your own if you have other thoughts!

What is the structure of your dataset?

The structure of the dataset includes 113,937 observations of 81 variables, meaning there are 113,937 individual loans oberved. We have created two new variables to better examine credit score. avgCreditScore takes the average of the upper and lower credit score to take the mean for each individual borrower. The new variable CSBucket is a categorical variable that will help determine how credit may influence loans.

What is/are the main feature(s) of interest in your dataset?

The main features of interest for me in the dataset include: Prosper Score: What factors contribute most, or have the highest correlation, to establshing a Prosper rating.

Also, is the LoanOriginalAmount for highly related to Income Range and credit score?

What other features in the dataset do you think will help support your
investigation into your feature(s) of interest?

I am also interested in what levels of credit scores influence the eventual borrower APR. Are there distinct patterns between the credit worthiness of a borrower and whether they get a loan?

Did you create any new variables from existing variables in the dataset?

Yes, I created the avgCreditScore variable to determine what number lies between the lower and upper credit score for each user. Then, I used the cut() function in order to bin the average credit scores per user.

Of the features you investigated, were there any unusual distributions?
Did you perform any operations on the data to tidy, adjust, or change the form
of the data? If so, why did you do this?

I had removed na’s and blank values from a number of individual datapoints in order to better run analysis such as bar graphs.

Bivariate Plots Section

Tip: Based on what you saw in the univariate plots, what relationships between variables might be interesting to look at in this section? Don’t limit yourself to relationships between a main output feature and one of the supporting variables. Try to look at relationships between supporting variables as well.

Loan original amount by Prosper Rating

## 
##     1     2     3     4     5     6     7 
##  6935  9795 14274 18345 15581 14551  5372

From the box plot above, we see that loans with Prosper Ratings of A, AA, and BB have much higher quartiles, outliers, and loan original amounts, which makes sense given that Prosper Ratings of C, D, E, HR are of lesser quality according to the Prosper website.

Let’s limit the ylim to further examine the median of the loan categories.

qplot(data = loans, y=loans$LoanOriginalAmount, x = loans$ProsperRating..Alpha., 
      geom='boxplot')+
  coord_cartesian(ylim = c(0,20000))+
  ggtitle('Loan Original Amount by Prosper Rating Alpha')

From the zoomed in data, we can see that AA loans have the highest median of any categoryat slightly above 10,000. Let’s run a table to see what the median # actually is.

by(loans$LoanOriginalAmount, loans$ProsperRating..Alpha., summary)
## loans$ProsperRating..Alpha.: 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    2500    4500    6159    7904   25000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: A
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    5850   10000   11460   15000   35000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: AA
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    6000   10940   11584   16000   35000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: B
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    6000   10000   11622   15000   35000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: C
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    5000   10000   10392   15000   25000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: D
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    4000    6100    7083   10000   15000 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: E
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    3600    4000    4586    5000   15900 
## -------------------------------------------------------- 
## loans$ProsperRating..Alpha.: HR
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    3000    4000    3463    4000   16800

The table above shows AA ratings with the median of 10,940, the highest of any category.

**Loan original amount by Delinquencies Last 7 Years* We’ve examined the loan original amount from the Prosper Rating, let’s see if borrower delinquencies have any effect on the loan original amount.

ggplot(data = loans, aes(x =loans$DelinquenciesLast7Years, y=loans$LoanOriginalAmount))+
  geom_point()+
  ggtitle('Loan Original Amount by Delinquencies Last 7 years')
## Warning: Removed 990 rows containing missing values (geom_point).

The plot above shows some obvious levels to the data, as Propser seems to provide loans in 5,000 increments, however, we do see a slight pattern in which, when Delinquencies in the last 7 years rise, the total amount of a loan often falls.

Let’s add transparency and jitter in order to account for overplotting.

ggplot(data = loans, aes(x =loans$DelinquenciesLast7Years, y=loans$LoanOriginalAmount))+
  geom_point(alpha = 1/30, position = "jitter")+
  ggtitle('Loan Original Amount by Delinquencies Last 7 years')
## Warning: Removed 990 rows containing missing values (geom_point).

The above chart, with it’s dark line on the y-axis at 0, shows that Prosper very much likes to provide loans to those with little to no delinquencies in the past 7 years. There are a few points at 99 in the chart, which may be an anomoly or human error, and is worth further questioning of Prosper’s data capture.

Loan original amount by Employment Status Building on the picture we are beginning to see with regards to loan original amount, let’s examine Employment status and loan original amount.

summary(loans$EmploymentStatus)
##                    Employed     Full-time Not available  Not employed 
##          2255         67322         26355          5347           835 
##         Other     Part-time       Retired Self-employed 
##          3806          1088           795          6134

In this data, I will create a new DF called loans_by_employmentstats as there are 2255 borrowers in which the status is blank, you can see this in the table abbove.

loans_by_employment <- subset(loans, loans$EmploymentStatus != "")
qplot(data = loans_by_employment, y=loans_by_employment$LoanOriginalAmount, x = loans_by_employment$EmploymentStatus, 
      geom='boxplot')+
  ggtitle('Loan Original Amount by Employment')

The boxplot above shows that employed Prosper borrowers, either through a company or self-employed, have higher median loan amounts than other categories, including Full-time and Part-time. This is odd, as employed persons are logically either employed full-time or part-time or self-employed. This is a question for Prosper as to what the classification methodology is.

qplot(data = loans_by_employment, y=loans_by_employment$LoanOriginalAmount, x = loans_by_employment$EmploymentStatus, 
      geom='boxplot')+
  coord_cartesian(ylim = c(0,20000))+
  geom_hline(yintercept = median(loans_by_employment$LoanOriginalAmount), color = "green")+
  ggtitle('Loan Original Amount by Number of Investors and Employment Status')

By placing the overall median line on the graph, we see that only the categories of “Employed” and “self-employed” actually have a higher median amount than the overall median, with the other categories falling behind.

Loan Original Amount by Estimated Return We’ve got a sense of the borrowers, now let’s take a look at the loan itself by examining the loan original amount and its estimated return.

ggplot(data = loans, aes(x=loans$EstimatedReturn, y=loans$LoanOriginalAmount))+
  geom_point(alpha = 1/20, position = 'jitter')+
  ggtitle('Loan Original Amount by Estimated Return')
## Warning: Removed 29084 rows containing missing values (geom_point).

The graph above, with slight transparency and jitter, show that the estimated return for most loans is falling around .05 and 1.5. Interestingly, there are a fair amount of loans that have negative returns, much more than those that have estimated returns of .2 or more.

A Pearson correlation test below shows a negative correlation of -.28. I would have predicted greater correlation, however, the negative number suggests as the loan original amount increases, the estimated return decreases, a common phenomenmon.

cor.test(loans$EstimatedReturn, loans$LoanOriginalAmount)
## 
##  Pearson's product-moment correlation
## 
## data:  loans$EstimatedReturn and loans$LoanOriginalAmount
## t = -86.98, df = 84851, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2922833 -0.2799279
## sample estimates:
##        cor 
## -0.2861175

Loan original amount by Investors

mean(loans$Investors)
## [1] 80.47523

By taking the mean amount of investors per loan, which is calculated to around 80, we can begin to see how many people it actually takes to get a Prosper loan fully-funed. A scatterplot can visualize this phenomeon.

ggplot(data = loans, aes(x = loans$Investors, y = loans$LoanOriginalAmount))+
  geom_point(alpha = 1/10)+
  geom_vline(xintercept = mean(loans$Investors), color = "green")+
  ggtitle('Loan Original Amount by Number of Investors')

The scatter plot above shows that, as loan amounts grow, so do the total amount of investors needed. The mean of just above 80 shows that the majority of loans are falling at a similar price level, thus a similar amount of investors are needed for analogous loans.

A correlation below shows a Pearson score of .38, lesser than what I expected.

cor.test(loans$Investors, loans$LoanOriginalAmount)
## 
##  Pearson's product-moment correlation
## 
## data:  loans$Investors and loans$LoanOriginalAmount
## t = 138.71, df = 113940, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3751140 0.3850494
## sample estimates:
##       cor 
## 0.3800926

Loan original amount by Credit Score

We will, finally, use our newly binned data to examine loan original amount by credit score bucket. This will provide a nice picture as to which credit score buckets have the highest median Loan Original amount.

qplot(data = loans, y=LoanOriginalAmount, x = csBucket, 
      geom='boxplot')+
  geom_hline(yintercept = median(loans$LoanOriginalAmount), color = "green")+
  ggtitle('Loan Original Amount by Credit Score Bucket')

Unsurprsiingly, the buckets of 700-800 and 800-900 both have medians that exceed the overall median. It is interesting to note that 600-700 credit scores have a median Loan Original Amount less than the overall median, an indication credit scores in this area are not deemed as worthy for a loan.

Bivariate Analysis

Tip: As before, summarize what you found in your bivariate explorations here. Use the questions below to guide your discussion.

Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?

Most interestingly, I discovered that a credit score of 600-700 has a substantially lower median loan original amount than credit scores of 700-800. This was surprising to me, as I suspected a slight decrease but, personally, have always considered a credit score of 600-700 to be somewhat trustworthy.

Also, the total amount of investors per loan was quite intriguing, as there were substantial outliers from the mean of 80 per loan. We will further examine this by exploring categories that may influence that in the multi-variate analysis portion.

Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)?

Yes, the relationship between employment status was particularly interesting, as “full time” employees have a signficiantly lower median loan amount than those simply categorized as “employed”. I suspect there may be an error in Prosper’s classification system.

What was the strongest relationship you found?

The relationship between total investors and dollar amount had a Pearson score of .38, the strongest relationship I uncovered.

Interestingly, loan original amount and estimated return were negatively correlated, showing that as a loan amount is greater, estimated returns are generally expected to fail.

Multivariate Plots Section

Tip: Now it’s time to put everything together. Based on what you found in the bivariate plots section, create a few multivariate plots to investigate more complex interactions between variables. Make sure that the plots that you create here are justified by the plots you explored in the previous section. If you plan on creating any mathematical models, this is the section where you will do that.

Examining loan original amound and borrower APR by Credit Score Bucket.

The above scatterplot shows that csBucket 800-900 are largely consolidated at a little less than .1 for their Borrower APR, despite loan amount. This shows that Prosper generally loans funds to those with good credit at various levels of dollar amount.

You can see distinct, almost vertical patterns of increased BorrowerAPR based on their credit score. Lower credit scores from 400-600 are largely consolidated lower on the y-axis at varying APRs, showing that credit scores that are lesser do not get loaned as large amounts as other credit scores.

Examining loan original amount and estimated return by Credit Score Bucket.

ggplot(data = subset(loans,!is.na(loans$csBucket)), aes(x = EstimatedReturn, y = LoanOriginalAmount))+
  geom_point(aes(color = csBucket))+
  ggtitle('Loan Original Amount by Estimated Return and Credit Score Bucket')
## Warning: Removed 28359 rows containing missing values (geom_point).

Similarly to our analysis on borrower apr, estimated returns are largely attributed to certain credit scores. The highest end of credit scores (800-900), have a distinct Estimated Return of around .05 percent, with 700-800 categories at around .075 to .1, and 600-700 following thereafter with growing estimated returns. This could be because those with higher credit scores pay their loans off quicker, at lower rates.

Interestingly, there are a bevy of loans at the 600-700 credit score level that do not pay off loans that are less than 10,000 in total value. Even though they have credit scores similarly to those borrowing at higher dollar amounts, they were unable to pay their comparable smaller debts.

**Loan Original Amount, # of Investors, Credit Score

ggplot(data = subset(loans,!is.na(loans$csBucket)), aes(x = Investors, y = LoanOriginalAmount))+
  geom_point(alpha = 1/3, aes(color = csBucket))+
  geom_vline(xintercept = median(loans$Investors))+
  ggtitle('Loan Original Amount by Number of Investors and Credit Score Bucket')

The graph above shows that the total amount of investors increases as the loan original amount increases, and invariably, the higher credit score users are more adept at getting additional investors. In the scatterplot, you hardly see any 400-700 credit score borrowers beyond the overall median line.

Interestingly, the higher end credit score borrowers of 800-900 generally have a # of investors per loan that is higher than the median and higher than there lesser counterparts, even twhen the loan original amount is the same, this means more individuals are investing smaller amounts per individual loan.

Loan Original Amount, Loan Investors, Prosper Rating

We run the tables below to view which Prosper Rating has the most loans and the highest loan amounts, we find that a score of 7 receives the highest median loan and a score of 1-2 have the lowest medians. This may be an indication of the loan worthiness of the borrowers - thus, we assue 7 to be the best loan for chance of repayment and 1 being the worse.

table(loans$ProsperRating..numeric.)
## 
##     1     2     3     4     5     6     7 
##  6935  9795 14274 18345 15581 14551  5372
by(loans$LoanOriginalAmount, loans$ProsperRating..numeric., summary)
## loans$ProsperRating..numeric.: 1
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    3000    4000    3463    4000   16800 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 2
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    3600    4000    4586    5000   15900 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 3
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    4000    6100    7083   10000   15000 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 4
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    5000   10000   10392   15000   25000 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 5
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    6000   10000   11622   15000   35000 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 6
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    5850   10000   11460   15000   35000 
## -------------------------------------------------------- 
## loans$ProsperRating..numeric.: 7
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    6000   10940   11584   16000   35000
ggplot(data = loans, aes(x = Investors, y = LoanOriginalAmount))+
  geom_point(alpha = 1/20, position = 'jitter', aes(color = loans$ProsperRating..numeric.))+
  geom_vline(xintercept = median(loans$Investors))+
  ggtitle('Loan Original Amount by Number of Investors and Numeric Prosper Rating')

The graph above shows that, as the number of investors and the loan original amount increases, more high-quality loans of Prosper Ratings of 4-5-6-7 are prevalent.

Delinquencies 7 Years Loan Investors, Prosper Rating Numeric

ggplot(data = loans_by_employment, aes(x = DelinquenciesLast7Years, y = LoanOriginalAmount))+
  geom_point(alpha = 1/2, position = 'jitter', aes(color = loans_by_employment$EmploymentStatus))+
  geom_vline(xintercept = mean(loans_by_employment$DelinquenciesLast7Years), color = 'black')+
  ggtitle('Loan Original Amount by Delinquencies Last 7 Years and Employment Status')
## Warning: Removed 88 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_vline).

When looking at the loan original amount and delinquencies the last 7 years, it is no surprise that the majority of points on the graph are those that are employed, even when transparency is added for overplotting. With the “employed” category as “red”, you will notice the prevalence of red dots as the loan amount increases, and the lack of red dots as the delinquencies the last 7 years increase below $5,000 loan amounts.

This means that those who are not categorized as “employed” in the Prosper system have higher delinquencies in the past 7 years, and do not get the same level of loan as those who are employed.

Multivariate Analysis

Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?

In this section, we wanted to look closer at what categories may be determining loan amounts, the amount of investors, and the delinquencies in the last 7 years. We noticed that those who were not categorized as “employed” saw themselves receiving loans of roughly less than 5,000. Those same individuals were likely to have a higher rate of delinquencies in the last 7 years than those categorized as “employed”, and their loan amounts were lesser than their employed counterparts even if the delinquencies in the last 7 years were the same.

We also discovered that Prospers numeric rating runs from 1-7, with 7 being the most trustworthy rating.

Were there any interesting or surprising interactions between features?

I was overall surprised to see that the number of investors increases as credit score and prosper rating increases. It was my inclination that if a loan were to be deemed safe or less risky, more investors would provide higher individual amounts towards that loan, thus, lowering the total amount of investors per loan.

OPTIONAL: Did you create any models with your dataset? Discuss the
strengths and limitations of your model.

We did not create any models with this dataset.


Final Plots and Summary

Tip: You’ve done a lot of exploration and have built up an understanding of the structure of and relationships between the variables in your dataset. Here, you will select three plots from all of your previous exploration to present here as a summary of some of your most interesting findings. Make sure that you have refined your selected plots for good titling, axis labels (with units), and good aesthetic choices (e.g. color, transparency). After each plot, make sure you justify why you chose each plot by describing what it shows.

Plot One

## Warning: Removed 88 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_vline).

Description One

The plot above shows the Loan Original Amount on the y-axis, the number of delinquencies in the last 7 years on the x-axis, with each plot indicating an employment status as a categorical variable.

This graph shows to me that, should you be employed, you have a marginal chance of receiving a loan from Prosper. Though the large majority of loans are at 0 delinquencies, it is important to notice that there are a great number of loans provided to people who have be delinquent dozens of times. You are more likely to receive a greater loan amount, however, if your employment status is “employed”

Plot Two

Description Two

The graph above shows the number of investors per loan on the x-axis, the total loan original amount on the y-axis, with the categorical variable of credit score bucket. This plot shows that, as the loan amount increases, the number of investors increases as well.

We already know from prior graphs that higher loan amounts are more likely to be people employed with no delinquencies on their account, couple that with higher credit scores and higher loan amounts are generally more safe. We see that, as loan amounts increase, the number of investors per loan also increases.

This, to me, is a strange phenomenmon, as I would have guessed that, if a loan were to be less risky, investors would invest greater amounts towards that loan, thus limiting the total amount of investors per loan.

The plot shows borrowers with credit scores between 700-900 are generally receiving more investors at higher loan amounts than other credit scores.

Plot Three

## Warning: Removed 28359 rows containing missing values (geom_point).

Description Three

The above plot shows the estimated return per loan on the x-axis, with the loan original amount on the y-axis and the credit score bucket as the categorical variable.

This plot shows that estimated returns will generally fall between .05 and .15, are nearly normally distributed, and will be somewhat dependent on the credit score of the borrower. Borrowers with higher credit scores are shown to provide less returns to investors, likely due to lower interest rates and ability to pay back a loan quickly.

The plot also shows that estimated returns for higher credit score borrowers are largely the same regardless of the loan amount, showing that loan amount does not really affect return rate, and vice versa.

Reflection

Tip: Here’s the final step! Reflect on the exploration you performed and the insights you found. What were some of the struggles that you went through? What went well? What was surprising? Make sure you include an insight into future work that could be done with the dataset.

The Prosper data was quite large and there were a number of variables that were omitted from this analysis simply due to time and expectations from the course. With greater time, one could examine the areas such as investment from friends to see if certain credit score users or certain Prosper loans are more likely to get loans from their friends.

It was interesting to note that there are a higher number of investors per loan, particularly when the credit score of the borrower is high. This goes against my intution that single or a handful of investors would want to buy out a loan completely. This potentially may show some skepticism of the Prosper platform.

I did not conduct any analysis of loan variables over time, as my questions were more focused on what affects a loan amount and the amount of investors investing in said loan. It may be interesting to explore whether estimated returns lowered or expanded overtime for Prosper loans.